6th Grade Solving One-Step Equations Worksheet Solutions (PDF)

6th Grade math worksheet solutions: Solving One-Step Equations – Maths PDF

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This one step equations answers for 6th Grade covers solving one-step equations (Common Core 6.EE.B.5, 6.EE.B.6, 6.EE.B.7), with a free PDF to print.

Check each equation solution here. The solutions show the inverse operation applied to both sides, a check by substitution, and the final answer in bold. Tape diagrams and balances illustrate several answers.

Grade 6 · Common Core State Standards: 6.EE.B.5, 6.EE.B.6, 6.EE.B.7

One step equations answers: exercises 1 to 10

Exercise 1 – Is it a solution? (addition)

$5 + 7 = 12$ is true.

Yes, 5 is a solution.

Exercise 2 – Is it a solution? (multiplication)

$3 \cdot 4 = 12$, and 12 is not 15.

No, 4 is not a solution.

Exercise 3 – Solve an addition equation

Subtract 9 from both sides: $x + 9 – 9 = 20 – 9$.

Check: $11 + 9 = 20$.

$x = 11$

Exercise 4 – Solve a subtraction equation

Add 6 to both sides: $x – 6 + 6 = 14 + 6$.

Check: $20 – 6 = 14$.

$x = 20$

Exercise 5 – Solve a multiplication equation

Divide both sides by 4: $x = 36 \div 4$.

Check: $4 \cdot 9 = 36$.

$x = 9$

Exercise 6 – Solve a division equation

Multiply both sides by 5: $x = 7 \cdot 5$.

Check: $35 \div 5 = 7$.

$x = 35$

Exercise 7 – Decimal addition

Subtract 3.5 from both sides: $x = 8.2 – 3.5 = 4.7$.

Check: $4.7 + 3.5 = 8.2$.

$x = 4.7$

Exercise 8 – Decimal multiplication

Divide both sides by 2.5: $x = 10 \div 2.5 = 4$.

Check: $2.5 \cdot 4 = 10$.

$x = 4$

Exercise 9 – Fraction addition

Subtract $\frac{1}{4}$: $x = \frac{3}{4} – \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$.

$x = \frac{1}{2}$

Exercise 10 – Fraction multiplication

Divide both sides by $\frac{2}{3}$, which is multiplying by $\frac{3}{2}$.

$x = 8 \cdot \frac{3}{2} = 12$. Check: $\frac{2}{3} \cdot 12 = 8$.

$x = 12$

Exercises 11 and up

Exercise 11 – Decimal subtraction

Add 2.75: $x = 5.25 + 2.75 = 8$.

$x = 8$

Exercise 12 – Write and solve (sum)

Equation: $n + 12 = 30$.

$n = 30 – 12 = 18$. Check: $18 + 12 = 30$.

$n = 18$

Both sides equal 30.

Exercise 13 – Write and solve (difference)

Equation: $n – 6 = 9$.

$n = 9 + 6 = 15$. Check: $15 – 6 = 9$.

$n = 15$

Exercise 14 – Money spent

Equation: $x – 14 = 23$.

$x = 23 + 14 = 37$.

$37.00

Exercise 15 – Tickets

Equation: $5t = 45$.

$t = 45 \div 5 = 9$.

$9.00 per ticket

Each ticket is $9.

Exercise 16 – Height

Equation: $h + 6 = 52$.

$h = 52 – 6 = 46$.

46 inches

Exercise 17 – Perimeter of a square

A square has 4 equal sides: $4s = 36$.

$s = 36 \div 4 = 9$.

9 feet

Exercise 18 – Equal groups

$4g = 24$.

$g = 24 \div 4 = 6$.

6 groups

Exercise 19 – Discount

$p – 8 = 27$.

$p = 27 + 8 = 35$.

$35.00

The original price is 27 + 8 = 35 dollars.

Exercise 20 – Saving plan

$x + 15 = 62$, so $x = 62 – 15 = 47$.

$6w = 54$, so $w = 54 \div 6 = 9$.

$47.00 saved at first; 9 weeks

Key facts behind this one step equations answers

Key facts

A solution makes an equation true; check by substituting.
Do the same operation to both sides to keep the equation balanced.
Use the inverse operation: add and subtract, multiply and divide.
Tape diagrams show addition and multiplication equations.
Write an equation from a story by naming the unknown with a variable.

How to use this one step equations answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

All Grade 6 chapters: Grade 6 math.

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