7th grade equations and inequalities
7th grade equations and inequalities (class 7): a quiz for kids, then every skill in order with lessons, a checklist and a plan.
🧒 Kids: answer 10 grade 7 equation questions. Tap Check ✓ after each one!
🔢 Equation practice 🏆 Equation levels 🧮 Equation solver ⚖️ Balance scale
What 7th grader learn about equations
In grade 7 (class 7), children solve two-step equations and inequalities. The numbers can be negative, fractions or decimals. They expand and simplify expressions with brackets, solve equations like 3x + 5 = 20 and −2x + 1 > 9, and turn real-world stories into equations.
- 7.EE.A.1: add, subtract, factor and expand linear expressions with rational coefficients.
- 7.EE.B.3: solve multi-step real-life problems with positive and negative numbers in any form.
- 7.EE.B.4a: solve equations like px + q = r and p(x + q) = r.
- 7.EE.B.4b: solve inequalities like px + q > r and graph the solutions.
The big idea in grade 7
Grade 7 is the year of two-step equations. Children solve equations like 3x + 5 = 20 and 2(x − 4) = 10, undoing each step in reverse order (7.EE.B.4a).
Numbers now include negatives, fractions and decimals, so integer and fraction skills matter. Children also expand and simplify expressions with rational coefficients (7.EE.A.1).
They solve two-step inequalities, flipping the sign when they multiply or divide by a negative, and use equations for real-world problems (7.EE.B.3 and 7.EE.B.4b).
When your child gets stuck
Most grade 7 trouble is not the algebra but the numbers. If −3x + 2 = 14 goes wrong, check the integer step on its own: is 14 − 2 = 12, and is 12 ÷ (−3) = −4?
If the integer rules are shaky, spend a week on 7th grade integers. The equations will feel much easier afterwards.
7th grade equation skills, in order
Work down the list. Each lesson explains the idea for parents with pictures and has a quiz for your child.
By the end of grade 7, your child should be able to…
- Simplify 3(x − 2) + 4x.
- Solve 4x + 7 = 31 and check the answer.
- Solve 2(x + 5) = 18.
- Solve (2/3)x = 10 and 0.5x − 1.5 = 4.
- Solve −3x + 2 > 14 and graph the answer.
- Write and solve an equation for a taxi or phone bill problem.
Unsure where your child is? The equation levels page has a short test for every step from expressions to systems.
A 4-week plan for 7th grade equations and inequalities
| When | Focus |
|---|---|
| Week 1 | Like terms and the distributive property, with negatives |
| Week 2 | Two-step equations, including brackets |
| Week 3 | Equations with fractions and decimals |
| Week 4 | Two-step inequalities and word problems |
Add 5 minutes a day with the equation practice tool. Check answers with the equation solver, which shows every step, and use the balance scale to see why both sides change together.
More for grade 7
All 7th grade math · CBSE class 7: Finding the Unknown · 7th grade integers · Equations quiz for grades 6 to 8 · Equations for kids
What to say to your child
A short script for teaching it the first time. Pause after each line and let your child do the next step.
- “Solve 3x + 5 = 20. What do we undo first?” (The + 5.)
- “So 3x = …?” (15.) “And x?” (5.)
- “Solve −2x > 8.” (x < −4: flip the sign.)
- “What is 2(x − 3) expanded?” (2x − 6.)
- “A gym costs $10 plus $15 a month. Write the cost.” (10 + 15m.)
More worked examples
Example 1: two steps: 5x − 4 = 21
Add 4: 5x = 25. Divide by 5: x = 5.
Example 2: brackets: 3(x + 2) = 24
Divide by 3: x + 2 = 8, so x = 6.
Example 3: inequality: −4x ≤ 20
Divide by −4 and flip: x ≥ −5.
Practice questions (answers below)
Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.
- 2x + 3 = 17
- 4x − 5 = 23
- x/3 + 2 = 8
- −3x + 1 = 13
- 2(x − 4) = 14
- 0.4x = 2
- Simplify 5(x + 1) − 2x
- 3x + 2 > 14
- −2x ≥ 10
- Stretch: (3/4)x − 2 = 7
Show the answers
- 7
- 7
- 18
- −4
- 11
- 5
- 3x + 5
- x > 4
- x ≤ −5
- 12
Common mistakes
How to teach it at home
Five minutes a day
Short daily practice beats long weekend sessions.
Number riddles
“I think of a number, double it and add 3. I get 17.” Riddles like this are equations in disguise.
Real bills
Phone plans, taxi fares and gym fees are all fixed cost plus a rate, perfect for writing equations.
By grade
- Before: 6th grade equations and expressions and 7th grade integers
- After: 8th grade equations
Not sure where to start?
The free 7th grade math check-up tests every grade 7 topic in 18–22 minutes. It shows which topics are solid and which lesson to start with.
Worksheets and practice
Two-step equations worksheet: printable PDF with an answer key.
Last reviewed
Questions parents ask
What equations should a 7th grader know?
Two-step equations like 3x + 5 = 20 and 2(x − 4) = 10, with negatives, fractions and decimals, plus two-step inequalities and word problems.
What is the difference between grade 6 and grade 7 equations?
Grade 6 solves one-step equations with whole numbers. Grade 7 solves two-step equations and inequalities with any rational numbers.
Is there a 7th grade equations quiz?
Yes. The quiz at the top of this page has 10 mixed grade 7 questions. Each one is marked straight away, with a hint for every mistake. Play again for a fresh set, or try the equations quiz for all three grades.
What is class 7 algebra?
Class 7 in India and grade 7 in the US cover similar algebra, though the order differs. This page lists the skills in order, starting with combining like terms, distributive property with variables, one-step equations.
How much equation practice does a 7th grader need?
About 10 minutes a day: 5 minutes on the current skill with the practice tool and 5 minutes of mixed review. Short daily practice works better than long weekly sessions.