Virginia SOL Math / Grade 7 / Patterns, Functions & Algebra

7.PFA.3

Two-Step Linear Equations

What you'll learn

  • Write two-step linear equations from situations
  • Solve two-step equations using inverse operations
  • Check a solution by substitution

Words to know

Equation —
a math sentence stating two expressions are equal
Variable —
a letter that stands for an unknown number
Inverse operation —
an operation that undoes another, like adding and subtracting
Solution —
the value that makes an equation true
Coefficient —
the number multiplied by the variable

Why it matters Two-step equations model real problems with a fixed part and a rate, such as a flat fee plus a cost per item, so solving them finds the unknown.

Worked examples

Model ItI do

Solve 2x + 3 = 11.

Undo the addition first: subtract 3 from both sides to get 2x = 8. Then undo the multiplication: divide both sides by 2 to get x = 4.

Try It TogetherWe do

Solve x over 3 minus 1 = 4.

Add 1 to both sides to get x over 3 = 5. Then multiply both sides by 3 to get x = 15.

Now YouYou do

Solve 5x minus 2 = 13.

Add 2 to both sides, then divide by 5. 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 + 5 = 13.

  2. 2.Solve 3x minus 4 = 11.

  3. 3.Solve x over 2 + 1 = 6.

On Level

The core Quick Check from the book.

  1. 1.Solve 3x + 4 = 19.

  2. 2.Solve 2x minus 5 = 9.

  3. 3.Solve x over 2 + 3 = 7.

  4. 4.Solve 4x + 1 = 17.

  5. 5.Check: is x = 6 a solution of 2x minus 1 = 11?

Challenge

Stretch your thinking.

  1. 1.Solve 5x minus 7 = 2x + 8.

  2. 2.A taxi charges a 3 dollar flat fee plus 2 dollars per mile. The total ride cost 17 dollars. How many miles was the ride?

  3. 3.Solve the quantity x + 4 over 3 = 5.