Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Write each step on its own line and name the operation you undo. Later problems ask for an estimate, a comparison of methods, and equations built from fees, rates and formulas.
Standards: 7.EE.B.3, 7.EE.B.4a · Level: Grade 7
Problem 2 Subtract, Then Multiply ★★★
Solve 5x − 4 = 31.
Problem 3 A Quotient Plus a Constant ★★★
Solve x4 + 3 = 9.
Problem 4 Read the Tape Diagram ★★★
The tape diagram shows 2x + 9 = 31. Find x.
Problem 5 A Negative Coefficient ★★★
Solve −4x + 6 = 30.
Problem 6 Decimal Coefficient ★★★
Solve 2.5x − 3.5 = 11.5.
Problem 7 Fraction Coefficient ★★★
Solve 78x + 5 = 19.
Problem 8 Two Ways with Parentheses ★★★
Solve 4(x + 3) = 36 two ways: dividing first, and distributing first.
Problem 9 Negative Factor Outside ★★★
Solve −2(x − 5) = 18.
Problem 10 Decimal Factor Outside ★★★
Solve 0.4(x − 3) = 2.8.
Problem 11 Negative Quotient ★★★
Solve −x3 − 4 = 2.
Problem 12 Variable on the Right ★★★
Solve 2.6 + 1.3x = −5.2.
Problem 13 Fractions Inside and Out ★★★
Solve 23(x + 34) = 52.
Problem 14 Arithmetic and Algebra ★★★
A number is multiplied by 6 and then 3.5 is subtracted, giving 20.5. Find the number by working backward with arithmetic, then by solving 6x − 3.5 = 20.5.
Problem 15 Summer Camp Cost ★★★
A summer camp charges a $60 registration fee plus $85 per week. Karim’s family paid $485 in total. Write an equation, estimate the number of weeks, and solve it.
Problem 16 Hours at the Food Truck ★★★
Ravi earns $9.75 per hour plus $30 in tips on Saturday. He earned $108 in all. How many hours did he work?
Problem 17 Fencing a Rectangle ★★★
A rectangular pen is x feet long and 6.5 feet wide. Its perimeter is 31 feet. Write and solve an equation for x.
Problem 18 Fahrenheit and Celsius ★★★
A science lab converts temperatures with F = 1.8C + 32. A thermometer reads 77°F. Find the Celsius temperature C.
Problem 19 Group Tickets with a Fee ★★★
A school buys 6 tickets. Each ticket costs t dollars plus a $2.50 booking fee, and the total is $87. Estimate t, then write and solve an equation to find it.
Problem 20 Descending the Trail ★★★
A hiker starts at an elevation of 1,240 feet and descends 36 feet each minute. After m minutes the elevation is 340 feet. Write and solve an equation, and state what the answer means.
