Virginia SOL Math / Grade 8 / Patterns, Functions & Algebra

8.PFA.4

Multistep Linear Equations

What you'll learn

  • Write multistep linear equations in one variable
  • Solve equations with variables on both sides
  • Solve practical problems using equations

Words to know

Equation —
a statement that two expressions are equal
Variable —
a symbol that stands for a number
Inverse operation —
an operation that undoes another
Coefficient —
the number multiplied by a variable
Solution —
the value that makes an equation true

Why it matters Multistep equations let us solve real problems where an unknown appears in several places or on both sides.

Worked examples

Model ItI do

Solve 3x + 5 = 20.

Subtract 5 from both sides: 3x = 15. Divide both sides by 3: x = 5. Check: 3 times 5 + 5 = 20, which is true.

Try It TogetherWe do

Solve 4x - 3 = 2x + 9.

Subtract 2x from both sides: 2x - 3 = 9. Add 3 to both sides: 2x = 12. Divide by 2: x = 6.

Now YouYou do

Solve 5x + 2 = 3x + 14.

Collect the variable terms on one side and the numbers on the other, then divide. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Solve 2x = 10.

  2. 2.Solve x + 7 = 12.

  3. 3.Solve 3x + 1 = 10.

On Level

The core Quick Check from the book.

  1. 1.Solve 2x + 7 = 15.

  2. 2.Solve 5x - 4 = 21.

  3. 3.Solve 3x + 1 = x + 9.

  4. 4.Solve 2(x + 3) = 16.

  5. 5.Solve 6x - 5 = 4x + 7.

Challenge

Stretch your thinking.

  1. 1.Solve 4x - 7 = 2x + 9.

  2. 2.Solve 3(x - 2) = 2x + 5.

  3. 3.The perimeter of a rectangle is 34. Its length is 3 more than its width. Find the width. (Perimeter is 2 times length plus 2 times width.)