Pre-algebra and algebraGrade 6
One-step equations worksheet with answer key
This sheet gives one-step equations in 2 columns with room for work and an answer line. Pick addition and subtraction, multiplication and division, or all four, and optionally add negatives or different letters.
- Fresh problems every time
- Answer key on its own page
- Print or PDF, Letter or A4
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On this page
The first real algebra
An equation says two things are equal, and solving it means finding the value that makes the statement true. A one-step equation needs a single move. If x + 8 = 15, something has been added to x, so subtract it from both sides. If 6x = 42, x was multiplied, so divide both sides. The key idea is the inverse operation: undo what was done, and do the same to both sides to keep the balance.
Sixth graders usually begin here after learning about expressions and variables. Each equation on this sheet has a little vertical space and an answer line already reading "x =" so students show the step instead of guessing.
Settings
- Equation type. The page opens on One-step. Change it to Two-step, Multi-step or Mixed if you want a different sheet.
- One-step operations. All four gives a blend. Addition and subtraction prints only x + a and x − a. Multiplication and division prints ax and x over a, where division is drawn as a fraction.
- Include negative numbers. Off by default, which keeps solutions positive. Turn it on once students are ready for answers like −5.
- Use different letters. Replaces x with y, n, a, m, k, p or t on each problem, so students learn that the letter is just a placeholder.
- Number of problems. 6 to 30, two per row.
Start with addition and subtraction, which most students grasp quickly, then move to multiplication and division. Because the numbers are random, a sheet may include a subtraction problem such as x − 9 = −7 even with negatives switched off. The right side can dip below zero when the added number is larger than the answer, so be ready for it.
Worked example: three equations
x − 9 = 14
- The 9 was taken away from x, so add 9 to both sides.
- x − 9 + 9 = 14 + 9, so x = 23.
- Check: 23 − 9 = 14. True.
7x = 56
- The 7 multiplies x, so divide both sides by 7.
- x = 56 ÷ 7 = 8.
- Check: 7 × 8 = 56. True.
x ÷ 4 = 6 (printed as x over 4)
- The 4 divides x, so multiply both sides by 4.
- x = 6 × 4 = 24.
- Check: 24 ÷ 4 = 6. True.
Notice that each solution uses the opposite of the operation that appears. Pairing the two (add with subtract, multiply with divide) is the single thing to memorize.
Using the key to diagnose
- Same operation instead of the opposite. For x − 9 = 14, an answer of 5 means the student subtracted 9 again. The key shows 23.
- Dividing the wrong way. For 7x = 56, an answer of 392 comes from multiplying by 7. Ask whether 7 times 392 equals 56.
- Only changing one side. A student who writes x = 14 + 9 and then leaves the left side unchanged has the right idea but needs the "both sides" habit made visible.
- No check. Encourage the substitution check, which catches most slips in a few seconds.
Where to go from here
When these feel automatic, step up to the two-step equations worksheet. Students who want more practice reading the structure of an expression can use the evaluating algebraic expressions worksheet. The fact fluency underneath, especially inverse facts, is built by the fact family worksheets.