Warm Up

 

A. Solving Two-Step Equations

Solving two-step equations involves the same processes used for solving one-step equations. Remember, there was a brief discussion of solving one-step equations in Unit 1.

Notice that the opposite operation is applied to both sides of the equation to isolate the variable.

Recall the opposite operation of addition is subtraction, and the opposite operation of multiplication is division.

Solving two-step equations involves applying more than one opposite operation.

Example 1

Solve the following equation for x.

«math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»12«/mn»«mi»x«/mi»«mo»+«/mo»«mn»45«/mn»«mo»=«/mo»«mn»189«/mn»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨» «semantics» «mstyle mathvariant=¨normal¨ mathsize=¨12.0pt¨ mathcolor=¨#000000¨» «mtable columnlines=¨none none¨ rowlines=¨none none none none none¨» «mtr» «mtd columnalign=¨left¨ rowalign=¨bottom¨» «mrow» «mn mathvariant=¨normal¨» «/mn» «/mrow» «/mtd» «/mtr» «/mtable» «/mstyle» «/semantics» «/math»

Step 1:
Undo the addition operation first by subtracting 45 from both sides of the equation.

Step 2:
Undo the multiplication operation by dividing both sides of the equation by 12.



Example 2

Solve the following equation for x. Express the answer to the nearest hundredth.


Step 1:
Undo the subtraction operation first by adding 35 to both sides of the equation.

 

Step 2:
Undo the division operation by multiplying both sides of the equation by 3.