A taxi charges $3.50 plus $2.10 per kilometre. A trip costs $24.50. How far was it?

3.5 + 2.1d = 24.5, so d = 10 km

Free worksheet · Australian Curriculum

Two-step equations worksheets with answers

A two-step equation takes two inverse operations to solve. Learn the order to do them in, then make a free worksheet with full solutions.

Make a worksheet ↓How to do it and a quick check ↓

Topic guide

Two-step equations, explained

Undo the operations in reverse order, do the same to both sides, and check your answer.

1. Undo in reverse order

In $3x + 5 = 20$ , the $x$ was multiplied by $3$ and then $5$ was added. Undo the $+5$ first, then the $\times 3$ :

$3x + 5 = 20, 3x = 15, x = 5$

2. Equations with division

Undo the subtraction, then multiply:

$\frac{x}{4} - 2 = 3, \frac{x}{4} = 5, x = 20$

3. Negative coefficients

Keep the sign with the number:

$7 - 2x = 1, -2x = -6, x = 3$

Dividing by $-2$ makes the answer positive here.

4. A bracket or fraction around the left side

If everything on the left is divided, multiply first:

$\frac{x + 4}{3} = 5, x + 4 = 15, x = 11$

5. Always check

Substitute your answer back in. For $x = 3$ in $7 - 2x = 1$ : $7 - 2(3) = 7 - 6 = 1$ , so it's right. Checking takes a few seconds and catches sign errors.

6. Word problems

A phone plan costs $15 a month plus $2 for each GB of data. One month's bill is $27. How much data was used?

$15 + 2g = 27, 2g = 12, g = 6$

So $6$ GB was used. Choose a letter for the unknown, write the equation, then solve.

Quick check: 10 questions

Try each one, then open the answer.

Solve $2x + 3 = 11$ .
Answer
$x = 4$
Solve $5x - 4 = 21$ .
Answer
$x = 5$
Solve $\frac{x}{3} + 2 = 6$ .
Answer
$x = 12$
Solve $4a + 7 = -5$ .
Answer
$a = -3$
Solve $\frac{x}{5} - 3 = 1$ .
Answer
$x = 20$
Solve $10 - 3x = 4$ .
Answer
$x = 2$
Solve $\frac{x - 2}{4} = 3$ .
Answer
$x = 14$
Solve $6y + 1.5 = 12.3$ .
Answer
$y = 1.8$
Solve $2(x + 3) = 18$ .
Answer
$x = 6$
A taxi charges $3.50 plus $2.10 per kilometre. A trip costs $24.50. How far was it?
Answer
$3.5 + 2.1d = 24.5$ , so $d = 10$ km

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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These topic pages cover this skill, with worked examples, common mistakes and a question to try.

Year 7 worksheetLinear equations Year 8 worksheetLinear equations and graphs Year 9 worksheetLinear equations and graphs Year 7 worksheetAlgebra

Questions

What is a two-step equation?

A two-step equation needs two inverse operations to solve, such as subtracting then dividing. For example, 3x + 5 = 20 is solved by subtracting 5, then dividing by 3.

Which step do you do first?

Undo the operations in the reverse order they were done to the unknown. Usually that means undoing adding or subtracting first, then multiplying or dividing.

How can students check their answer?

Substitute the answer back into the original equation. If both sides are equal, the answer is correct.

More skill worksheets

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