AlgebraStructure & Method · Book 1All Chapters

Transforming Equations

3-3Using Several Transformations

Overview

Use multiple steps in order: simplify each side, then undo addition/subtraction, then undo multiplication/division.

Key ideas

  • Combine like terms first.
  • Undo addition/subtraction before multiplication/division.
  • Check by substitution.

Worked examples

Example 1

Problem. Solve 3x + 4 = 19.

Solution. Subtract 4: 3x = 15. Divide by 3: x = 5.

Example 2

Problem. Solve 5 − 2y = 13.

Solution. Subtract 5: −2y = 8. Divide by −2: y = −4.

Practice

Try each one. Click Show answer when ready.

  1. 1.

    Solve 2x − 7 = 11.

  2. 2.

    Solve 4 + 3n = −5.

  3. 3.

    Solve (x/2) + 6 = 10.

Challenge problems

A little tougher — great for test prep. Click Show answer when ready.

  1. 1.

    Solve: 2x + 5 = 17.

  2. 2.

    Solve: 3 − 4x = 19.