These twenty-two problems practice Common Core standards 8.EE.C.7a and 8.EE.C.7b. Solve multi-step linear equations with whole numbers, negatives, fractions and decimals, and use the distributive property and like terms.
You will also decide whether an equation has one solution, no solution or infinitely many solutions. The last six are word problems that need you to write and solve an equation.
Problem 1: Add then multiply
Solve \(4x+7=31\).
Problem 2: Negative coefficient
Solve \(-3x+8=-10\).
Problem 3: Fraction coefficient
Solve \(\frac{x}{4}-3=5\).
Problem 4: Distribute first
Solve \(3(2x-1)=45\).
Problem 5: Variables on both sides
Solve \(5x+4=3x+16\).
Problem 6: Collect the x terms
Solve \(7x-2=4x+13\).
Problem 7: Variable with a negative
Solve \(9-2x=x+21\).
Problem 8: Distribute and collect
Solve \(4(x-3)=2x+6\).
Problem 9: Combine like terms
Solve \(3x+2(x-4)=17\).
Problem 10: Fraction equation
Solve \(\frac{2}{3}x+1=9\).
Problem 11: Fractions on both sides
Solve \(\frac{1}{2}x-3=\frac{1}{4}x+2\).
Problem 12: Decimal equation
Solve \(0.4x+1.5=0.1x+4.8\).
Problem 13: Fraction times parentheses
Solve \(\frac{3}{4}(x-8)=9\).
Problem 14: No solution
Solve \(4x+6=4x+9\). Explain your result.
Problem 15: Infinitely many
Solve \(3(x+2)=3x+6\). Explain your result.
Problem 16: Sort the equations
Tell whether each equation has one solution, no solution or infinitely many solutions. Solve if there is one solution.
- \(5(x-1)=2x+10\)
- \(7x-3=7x+2\)
- \(2(4x+3)=8x+6\)
Problem 17: Gym memberships
Jamal’s gym charges $15 to join plus $4 per visit. Sofia’s gym charges $9 to join plus $6 per visit. After how many visits do both memberships cost the same, and what is that cost?
Problem 18: Taxi rates
Cab A charges $3.50 plus $2 per mile. Cab B charges $2 plus $2.50 per mile. For what trip length are the fares equal, and what is the fare?
Problem 19: Rectangle perimeter
A rectangular garden is \(2x+3\) feet long and \(x\) feet wide. Its perimeter is 48 feet. Find \(x\) and the length and width of the garden.
Problem 20: Saving up
Aisha has $40 and saves $12 each week. Diego has $100 and saves $7 each week. After how many weeks will they have the same amount? How much is that?
Problem 21: Number puzzle
Three times the sum of a number and 4 equals 5 times the number minus 6. Write an equation and find the number.
Problem 22: Burning candles
Candle A is 12 inches tall and burns 0.5 inch per hour. Candle B is 9 inches tall and burns 0.25 inch per hour. After how many hours are the candles the same height, and how tall are they?
See every chapter on the Grade 8 math page.