Equations
One-step equations worksheet with integers
Print a 10-question one-step equations worksheet with signed integers, four inverse operations, exact answers, worked steps, and substitution checks.
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Two-step equations worksheet
Print a 10-question two-step equations worksheet with integer quantities, fractional coefficients, grouped quotients, worked answers, and exact checks.
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Solve the equation and round the final answer to the nearest hundredth when needed. Integer operands do not guarantee an integer solution; a fractional coefficient may also appear.
Download the practice pages alone, or include a separate answer key or teacher model. Longer activities may use more than one page.
Customize this worksheetKeep exact working separate from final rounding
These equations can have fractional or recurring-decimal solutions. The worksheet asks for the nearest hundredth; the key also retains an exact solution, shows the intermediate equations and substitutes the exact value back into the original relationship.
A rounded decimal is a report of the solution, not necessarily an exact substitute for it. Round only at the end. In the two-step sets, a fractional coefficient may appear alongside integer or decimal constants.
Learning objective
What this activity builds
Identify the order of two operations acting on an unknown and undo them while preserving equality.
Worked example
Solve (7 − x) ÷ 3 = 5.
x = −8.
Multiply both sides by 3 to obtain 7 − x = 15. Subtract 7: −x = 8. Divide by −1: x = −8. Check: (7 − (−8)) ÷ 3 = 15 ÷ 3 = 5.
Teaching notes
Make the practice count
- Identify what the fraction bar groups before choosing the first operation.
- Contrast 7 − x with x − 7.
- Keep fractional coefficients exact until the equation is solved.
- Check a negative answer rather than rejecting it because the visible constants are positive.
When to use this two-step equations worksheet
Use this ten-question set after learners can solve one-step signed equations. It combines equations such as ax + b = c with fractional coefficients and grouped quotients such as (x + b) ÷ a and (b − x) ÷ a. Learners practice reading the grouping before choosing an inverse operation.
The equation mix and question count are not selectable. Choose the two-step decimal equations worksheet instead when you want decimal quantities printed in the problems; this set emphasizes integer quantities while still requiring exact fraction work.
Does “integer” mean every answer is an integer?
No. Fractional coefficients and the generated integer quantities can produce non-integer solutions. The answer key preserves the exact value and also reports the result to the nearest hundredth.
What should learners check before rounding?
Substitute the exact solution into the original equation, especially when the variable appears second in b − x. Round only the final reported value, not the value used in the check.
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Includes affine, fractional-coefficient, and grouped-numerator equations. Exact solutions remain visible on the key.
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