Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Work from easy equations to modeling problems. Show each balance step, check your answers by substituting, and explain when a variable disappears.
Standards: 8.EE.C.7a, 8.EE.C.7b · Level: Grade 8
Problem 2 Variable on both sides ★★★
Solve 3x + 7 = 2x + 15.
Problem 3 Distribute first ★★★
Solve 4(x + 3) = 32.
Problem 4 Combine like terms ★★★
Solve 6x − 2x + 9 = 25.
Problem 5 Fraction coefficient ★★★
Solve 23x = 18.
Problem 6 Balance scale ★★★
The scale is balanced. Write the equation it shows and find the weight of one x tile.
Problem 7 Both sides variable ★★★
Solve: (a) 7x − 5 = 3x + 19 (b) 9 − 2x = 5x − 12
Problem 8 Distribute on both sides ★★★
Solve 3(2x − 5) = 2(x + 7).
Problem 9 Clear the fractions ★★★
Solve x2 + x5 = 14.
Problem 10 Decimal coefficients ★★★
Solve 0.5x + 3.2 = 1.3x − 0.8.
Problem 11 How many solutions? ★★★
Decide whether each equation has one solution, no solution or infinitely many solutions: (a) 4x + 6 = 4x + 9 (b) 3(x + 2) = 3x + 6 (c) 5x − 1 = 2x + 8
Problem 12 Choosing k ★★★
Find the value of k that makes (a) 6x + 5 = kx − 3 have no solution, and (b) 4x + 7 = kx + 7 have infinitely many solutions.
Problem 13 Rational coefficient ★★★
Solve 78(x + 4) = 14.
Problem 14 Graph and equation ★★★
The two lines drawn below stand for the sides of 3x − 2 = x + 4. Read the x-coordinate where they meet, then confirm it by solving the equation.
Problem 15 Gym membership ★★★
Gym A charges a $25 sign-up fee plus $18 per month. Gym B has no sign-up fee and charges $23 per month. After how many months do the two gyms cost the same? What is that cost?
Problem 16 Two taxi companies ★★★
Company A charges $4 plus $2.50 per mile. Company B charges $1.60 plus $3.10 per mile. For what distance do both charge the same, and what is that charge?
Problem 17 Garden rectangle ★★★
A rectangular garden has length 3x + 2 feet and width x + 5 feet. Its perimeter is 62 feet. Find x and the garden’s length and width.
Problem 18 Consecutive odd integers ★★★
The sum of three consecutive odd integers is 87. Write an equation and find the integers.
Problem 19 What does 8 = 8 mean? ★★★
Kai solved 2(x + 4) = 2x + 8 and got 8 = 8, so he wrote x = 8. Explain his mistake, state the correct conclusion, and write one equation of your own that has no solution.
Problem 20 Fractions on both sides ★★★
Solve 3x − 24 + 1 = x + 72.
