What is included in the answer key?

By default, each problem has a worked solution, a reason for each solving step, and a check in the original equation. Choose Answers only for final answers without the worked steps.

How do the difficulty settings differ?

Every setting has eight problems and the same two solving steps. Easier and on level have two noninteger solutions and integer right-hand sides. Harder has five noninteger solutions and can have fractions or decimals on the right.

Does a zero on the right mean the answer is zero?

No. Each sheet includes one zero solution and a different equation with zero on the right. For example, 2(x - 1) = 0 has solution x = 1. Divide first, then undo the operation inside the group.

Can my child use a different method?

Yes. Expanding first is also valid when the operations are correct. The key shows how to undo the multiplication outside the parentheses first.

7th grade solving grouped equations

7th grade solving grouped equations worksheets

A grouped equation has a factor multiplying an expression in parentheses, such as 6(x - 1) = -42. Students solve for the unknown by undoing the multiplication, then the addition or subtraction. This sheet includes signed integers and fractions. The default key includes a worked solution and substitution check for every problem. Easier uses smaller numbers and fewer negative factors. On level mixes signed integer factors with halves and quarters. Harder includes more fractional solutions, more negative factors and two problems written with decimals.

Free printable PDF worksheet, aligned to Common Core 7.EE.B.4.a.

Each print is a different sheet with its own answer key. You don't need to sign up.

The kind of problems you'll get

Solve each equation. Show your steps, then check your answer in the original equation.

6 × (x − 1) = −66
Answer: x = −10
2 × (e + 5) = 14
Answer: e = 2
−6 × (x − 2) = 60
Answer: x = −8

Every print pulls a fresh set of problems at this level, so a make-up test or a second sibling never gets the same sheet.

What's on a 7th grade sheet

Solving grouped equations. Solve each equation. Show your steps, then check your answer in the original equation. 8 problems per page.

Every version prints on US Letter or A4, with its answer key after the problems.

How to teach this

Ask your child which operation acts on the whole group first. Divide both sides by that factor, then isolate the variable. Have them substitute the answer into the original equation. If they expand the parentheses first, check that each step preserves equality; that method can also give a correct solution.

Watch for: Dividing one side changes the equation. Apply the same operation to both sides. Keep track of the sign outside the parentheses. Dividing by a negative number can change the sign of the value on the right.

Common questions about 7th grade solving grouped equations

What is included in the answer key?: By default, each problem has a worked solution, a reason for each solving step, and a check in the original equation. Choose Answers only for final answers without the worked steps.
How do the difficulty settings differ?: Every setting has eight problems and the same two solving steps. Easier and on level have two noninteger solutions and integer right-hand sides. Harder has five noninteger solutions and can have fractions or decimals on the right.
Does a zero on the right mean the answer is zero?: No. Each sheet includes one zero solution and a different equation with zero on the right. For example, 2(x - 1) = 0 has solution x = 1. Divide first, then undo the operation inside the group.
Can my child use a different method?: Yes. Expanding first is also valid when the operations are correct. The key shows how to undo the multiplication outside the parentheses first.

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Aligned to Common Core 7.EE.B.4.a. Reviewed by the One more sheet team. Content version 241, updated October 2026.

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