Pythagorean Theorem Problem Solving- Getting Into It

Lesson 2: Pythagorean Theorem Problem Solving - Getting Into It

   Getting Into It

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 Chapter 1, Lesson 1 Getting Into It.

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.

   Multimedia

A video describing two-step equations is provided.

EXAMPLE 1

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Solve for x.

12x + 45 = 189 12x + 45 - 45 = 189 - 45 12x + 45 - 45 = 189 - 45 12x = 144	Step 1: Undo the addition operation first by subtracting 45 from both sides of the equation.
12x ÷ 12 = 144 ÷ 12 12x ÷ 12 = 144 ÷ 12 x = 12	Step 2: Undo the multiplication operation by dividing both sides of the equation by 12.

Task

Solve the following equations for the indicated variable.

1. 49y + 7 = 399
2. x² + 90 = 315 (Hint: remember that the opposite operation of squaring is to use the square root)

Solutions

1. 49y + 7 = 399
   49y + 7 - 7 = 399 - 7
   49y = 392
   49y/49 = 392/49
   y = 8


2. x² + 90 = 315
   x² + 90 - 90 = 315 - 90
   x² = 225
   √x² = √225
   x = 15

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