Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Write every sign carefully, and use a test value to check any answer that feels uncertain. The final six problems place the algebra inside gardens, prices, fundraisers and trails.
Standards: 7.EE.A.1, 7.EE.A.2 · Level: Grade 7
Problem 2 Expand a Sum ★★★
Expand 6(x + 7).
Problem 3 Expand a Difference ★★★
Expand 5(2a − 3).
Problem 4 Test for Equivalence ★★★
Jaylen claims that 7(x + 2) equals 7x + 2. Fill in every blank of the table to test his claim, then say whether he is right and give the correct expansion.
Problem 5 Expand with a Negative Factor ★★★
Expand −3(4x − 5).
Problem 6 Combine Terms in Four Pieces ★★★
Simplify 8x − 3 + 2x + 11 − 5x.
Problem 7 Expand with a Fraction ★★★
Expand 34(8x − 12).
Problem 8 Expand with a Decimal ★★★
Expand −0.5(6x + 9.2).
Problem 9 Factor from an Area Model ★★★
A rectangle is split into two parts with areas 18x and 24, as shown. Find the greatest common factor and write 18x + 24 in factored form.
Problem 10 Factor with a Negative GCF ★★★
Factor −8x − 20 so that the first term inside the parentheses is positive.
Problem 11 Subtract an Expression ★★★
Simplify (3x + 2) − (5x − 7).
Problem 12 Add Fractional Coefficients ★★★
Simplify (23x + 14) + (13x − 34).
Problem 13 Two Distributions Then Combine ★★★
Simplify 4(2x − 3) + 6(x + 1.5).
Problem 14 Factor a Decimal Expression ★★★
Write 1.5x − 4.5 as 1.5 times a binomial.
Problem 15 Perimeter of a Garden ★★★
A herb bed measures (5x + 1) feet by (2x + 4) feet. Write a simplified expression for the fencing needed around it, then find the length of fencing when x = 2.
Problem 16 Price with Sales Tax ★★★
A jacket costs p dollars before 8% sales tax. Write the total cost as a single product, then find the total for a $45 jacket.
Problem 17 Clearance Discount ★★★
A skateboard has a regular price of p dollars and is marked 35% off. Write the sale price as one product, then find the sale price when the regular price is $80.
Problem 18 Fundraiser Revenue ★★★
A club sells shirts for x dollars each and hats for (x − 4) dollars each. It sells 15 shirts and 25 hats. Write and simplify an expression for the total revenue. Then find the revenue when x = 18.
Problem 19 Find the Error ★★★
Two students simplified 3(2x − 4) − 2(x − 5). Ines wrote 4x − 2 and Cal wrote 4x − 22. Decide who is correct, check with x = 3, and describe the other student’s error.
Problem 20 Three Trail Sections ★★★
A hiking trail has three sections. Section 1 is (2x + 1.5) miles. Section 2 is 34 as long as section 1. Section 3 is (x − 0.25) miles shorter than section 1. Write a simplified expression for the whole trail, then find its length when x = 2.
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