Virginia SOL Math / Grade 6 / Patterns, Functions & Algebra

6.PFA.3

One-Step Equations

What you'll learn

  • Write one-step linear equations from a context
  • Solve one-step linear equations using inverse operations
  • Check solutions by substitution

Words to know

Equation —
a math sentence with an equal sign
Variable —
a letter that stands for an unknown number
Inverse operation —
an operation that undoes another
Solution —
the value that makes an equation true
Coefficient —
the number multiplied by a variable

Why it matters Equations turn a word problem into a solvable sentence, so we can find an unknown length, price, or amount.

Worked examples

Model ItI do

Solve x + 7 = 12.

Undo the addition by subtracting 7 from both sides: x + 7 - 7 = 12 - 7, so x = 5. Check: 5 + 7 = 12, which is true.

Try It TogetherWe do

Solve 4x = 20.

Undo the multiplication by dividing both sides by 4: 4x divided by 4 = 20 divided by 4, so x = 5. Check: 4 times 5 = 20.

Now YouYou do

Solve x - 3 = 9.

Undo the subtraction by adding 3 to both sides. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Solve x + 4 = 9.

  2. 2.Solve x - 2 = 7.

  3. 3.Solve 5x = 30.

On Level

The core Quick Check from the book.

  1. 1.Solve x + 5 = 11.

  2. 2.Solve x - 6 = 4.

  3. 3.Solve 3x = 18.

  4. 4.Solve x divided by 2 = 7.

  5. 5.A number plus 8 equals 15. Write and solve an equation for the number.

Challenge

Stretch your thinking.

  1. 1.Solve x divided by 4 = 8.

  2. 2.A number times 7 equals 63. Write and solve an equation for the number.

  3. 3.Marco had some marbles and lost 12, leaving him 25. Write and solve an equation for how many he started with.