Lesson 7 — Activity 3: Solving an Equation
Lesson 7 — Activity 3: Solving an Equation
Getting Ready
In this lesson, you will take what you have learned so far about algebra, variables, and constants to solve equations.
Try This:
Answer the following algebraic equations:
4 + d = 10
4 – d = 2
4 + 6 = 10
4 – 2 = 2
Sometimes in algebra, instead of being given a number to substitute for the variable, we have to find out what the variable is.
Look at this example: d + 2 = 6
Here, we have to work out what number we would use for d to solve this equation. Even though we can probably do this one in our heads, there are steps that we need to follow. Learning these steps with an easy example will help us with more difficult equations.
The key is to
ALWAYS get the variable by itself on one side of the equation.
Follow these steps to do this:
- Decide which numbers have to be removed to leave the variable by itself. In this case, the + 2 has to go (d + 2 = 6) to leave the d by itself.
- If we subtract 2 from the d + 2, we will end up with the d by itself.
IT IS VERY IMPORTANT THAT WE DO THIS TO BOTH SIDES OF THE EQUATION!
To keep the equation accurate, we must subtract 2 from EACH side as follows:
d + 2 = 6 (our original question)
d + 2 – 2 = 6 – 2
d + 0 = 4
d = 4
Let's check our answer:
Does 4 + 2 = 6? Yes it does! Our answer is correct!
Let's try another example:
d – 2 = 4
d – 2 = 4 (our original question)
d – 2 + 2 = 4 + 2
d + 0 = 6
d = 6
Let's check our answer:
Does 6 – 4 = 2? Yes it does! Our answer is correct!
Once we have the variable by itself on one side of the equal sign and have a single constant on the other side of the equal sign, we have solved the equation!
Now you try it! Solve for y in the following equation:
y + 10 = 31
Get the variable y on one side of the equation by itself. To do this, we subtract 10 from each side as follows:
y + 10 – 10 = 31 – 10
Our equation now reads:
y + 0 = 21
y = 21
Let's check to see if we are correct:
Does 21 + 10 = 31? Yes, it does! We are correct!
Solve for z in the following equation:
z – 10 = 7
Get the variable z on one side of the equation by itself. To do this, we add 10 to each side as follows:
z – 10 + 10 = 7 + 10
Our equation now reads:
z – 0 = 17
z = 17
Let's check to see if we are correct:
Does 17 – 10 = 7? Yes, it does! We are correct!
Self-check!
Try this!
Try this activity to practice solving for the variable. Answer these questions on your own first. When you are finished, click on the tabs below to check your answers
Solve for y in the following equation: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»+«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»10«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»31«/mn»«/mstyle»«/math»
Step 1: Get the variable y on one side of the equation by itself. You need to get rid of the 10 to leave 3y by itself. To do this you subtract 10 from each side.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»+«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»10«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»-«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»31«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»-«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«/mrow»«/mstyle»«/math»
The 10's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo»+«/mo»«mo»§#160;«/mo»«mn»10«/mn»«/menclose»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo»-«/mo»«mo»§#160;«/mo»«mn»10«/mn»«/menclose»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»31«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»-«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»10«/mn»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»21«/mn»«/mstyle»«/math»
Step 2: y is not by itself yet because of the 3. Since 3 is multiplying by y, to get rid of the 3 you can divide each sides by 3 .
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mfrac mathcolor=¨#62D3B3¨»«mrow»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«/mrow»«mn»3«/mn»«/mfrac»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mfrac mathcolor=¨#62D3B3¨»«mn mathcolor=¨#FFFFFF¨»21«/mn»«mn»3«/mn»«/mfrac»«/mstyle»«/math»
The 3's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»3«/mn»«/menclose»«mi mathsize=¨16px¨»y«/mi»«/mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»3«/mn»«/menclose»«/mfrac»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»=«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mfrac mathcolor=¨#FFFFFF¨»«mn mathsize=¨16px¨»21«/mn»«mn mathsize=¨16px¨»3«/mn»«/mfrac»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»7«/mn»«/mrow»«/mstyle»«/math»
Step 1: Get the variable y on one side of the equation by itself. You need to get rid of the 10 to leave 3y by itself. To do this you subtract 10 from each side.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»+«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»10«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»-«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»31«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»-«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»10«/mn»«/mrow»«/mstyle»«/math»
The 10's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo»+«/mo»«mo»§#160;«/mo»«mn»10«/mn»«/menclose»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo»-«/mo»«mo»§#160;«/mo»«mn»10«/mn»«/menclose»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»31«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»-«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»10«/mn»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»21«/mn»«/mstyle»«/math»
Step 2: y is not by itself yet because of the 3. Since 3 is multiplying by y, to get rid of the 3 you can divide each sides by 3 .
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mfrac mathcolor=¨#62D3B3¨»«mrow»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mi mathcolor=¨#FFFFFF¨»y«/mi»«/mrow»«mn»3«/mn»«/mfrac»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mfrac mathcolor=¨#62D3B3¨»«mn mathcolor=¨#FFFFFF¨»21«/mn»«mn»3«/mn»«/mfrac»«/mstyle»«/math»
The 3's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»3«/mn»«/menclose»«mi mathsize=¨16px¨»y«/mi»«/mrow»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»3«/mn»«/menclose»«/mfrac»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»=«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mfrac mathcolor=¨#FFFFFF¨»«mn mathsize=¨16px¨»21«/mn»«mn mathsize=¨16px¨»3«/mn»«/mfrac»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»y«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»7«/mn»«/mrow»«/mstyle»«/math»
Solve for p in the following equation: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mfrac mathcolor=¨#FFFFFF¨»«mi»p«/mi»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»-«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»8«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»3«/mn»«/mstyle»«/math»
Step 1: Get the variable p on one side of the equation by itself. You need to get rid of the 8 to leave p/4 by itself. To do this you add 8 to each side.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mi»p«/mi»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»-«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»8«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»8«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»8«/mn»«/mrow»«/mstyle»«/math»
The 8's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mi mathsize=¨16px¨»p«/mi»«mn mathsize=¨16px¨»4«/mn»«/mfrac»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo mathsize=¨16px¨»-«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»8«/mn»«/menclose»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo mathsize=¨16px¨»+«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»8«/mn»«/menclose»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»=«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»3«/mn»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»+«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»8«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mi»p«/mi»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»11«/mn»«/mrow»«/mstyle»«/math»
Step 2: p is not by itself yet because of the 4. Since it is dividing by 4, to get rid of the 4 you can multiply each side by 4.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mi»p«/mi»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»§#215;«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»4«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»11«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»§#215;«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»4«/mn»«/mrow»«/mstyle»«/math»
The 4's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mi mathsize=¨16px¨»p«/mi»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»4«/mn»«/menclose»«/mfrac»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo mathsize=¨16px¨»§#215;«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»4«/mn»«/menclose»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»=«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»11«/mn»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#215;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»4«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»p«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»44«/mn»«/mrow»«/mstyle»«/math»
Step 1: Get the variable p on one side of the equation by itself. You need to get rid of the 8 to leave p/4 by itself. To do this you add 8 to each side.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mi»p«/mi»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»-«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»8«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»8«/mn»«mo»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»3«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»+«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»8«/mn»«/mrow»«/mstyle»«/math»
The 8's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mi mathsize=¨16px¨»p«/mi»«mn mathsize=¨16px¨»4«/mn»«/mfrac»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo mathsize=¨16px¨»-«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»8«/mn»«/menclose»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo mathsize=¨16px¨»+«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»8«/mn»«/menclose»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»=«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»3«/mn»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»+«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»8«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mi»p«/mi»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»11«/mn»«/mrow»«/mstyle»«/math»
Step 2: p is not by itself yet because of the 4. Since it is dividing by 4, to get rid of the 4 you can multiply each side by 4.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mfrac mathcolor=¨#FFFFFF¨»«mi»p«/mi»«mn»4«/mn»«/mfrac»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»§#215;«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»4«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»11«/mn»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#62D3B3¨»§#215;«/mo»«mo mathcolor=¨#62D3B3¨»§#160;«/mo»«mn mathcolor=¨#62D3B3¨»4«/mn»«/mrow»«/mstyle»«/math»
The 4's on the left side cancel each other. Therefore you are left with:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#FFFFFF¨»«mi mathsize=¨16px¨»p«/mi»«menclose notation=¨updiagonalstrike¨»«mn mathsize=¨16px¨»4«/mn»«/menclose»«/mfrac»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«menclose notation=¨updiagonalstrike¨ mathcolor=¨#FFFFFF¨»«mo mathsize=¨16px¨»§#215;«/mo»«mo mathsize=¨16px¨»§#160;«/mo»«mn mathsize=¨16px¨»4«/mn»«/menclose»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»=«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»11«/mn»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#215;«/mo»«mo mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathsize=¨16px¨ mathcolor=¨#FFFFFF¨»4«/mn»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨16px¨»«mrow»«mi mathcolor=¨#FFFFFF¨»p«/mi»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mo mathcolor=¨#FFFFFF¨»=«/mo»«mo mathcolor=¨#FFFFFF¨»§#160;«/mo»«mn mathcolor=¨#FFFFFF¨»44«/mn»«/mrow»«/mstyle»«/math»
Digging Deeper