These twenty problems practice Common Core standards 7.EE.B.3 and 7.EE.B.4a. Solve equations of the form px + q = r and p(x + q) = r with whole numbers, negatives, decimals and fractions. The last six are word problems that ask you to write an equation first, solve it, and check that the answer makes sense. Work from easiest to hardest.
Problem 1: Add, then multiply
Solve \(3x+4=19\).
Problem 2: Six groups plus five
Solve \(6x+5=47\).
Problem 3: Subtract, then divide
Solve \(5x-8=27\).
Problem 4: Divide, then subtract
Solve \(\frac{x}{5}-2=6\).
Problem 5: A division step
Solve \(\frac{x}{4}+3=10\).
Problem 6: Below zero
Solve \(3x+14=2\). Then plot the solution on the number line.
Problem 7: A negative solution
Solve \(2x+7=1\). Then plot the solution on a number line.
Problem 8: Two negatives
Solve \(-5x-7=18\).
Problem 9: A negative coefficient
Solve \(-3x+5=-10\).
Problem 10: Decimal coefficient
Solve \(0.6x+2.4=7.8\).
Problem 11: Parentheses
Solve \(4(x+3)=36\) by dividing first. Then solve it again by distributing first, and compare.
Problem 12: Decimal in parentheses
Solve \(5(x-2.5)=20\).
Problem 13: Fraction coefficient
Solve \(\frac{3}{4}x-2=7\).
Problem 14: Estimate, then solve
Solve \(2.5x+1.5=11\). First estimate: decide whether \(x\) is a little more or a little less than 4, and explain why. Then solve exactly.
Problem 15: Saving for a bike
Jamal has \(\$45\) and saves \(\$8\) each week. After \(w\) weeks he has \(\$93\). Write an equation and find \(w\).
Problem 16: Rectangle perimeter
A rectangle is \(6\text{ in}\) wide. Its perimeter is \(40\text{ in}\). Write an equation of the form \(2(x+6)=40\) for the length \(x\) and solve it. Then solve the problem again with arithmetic.
Problem 17: Movie night
Three friends each buy a movie ticket costing \(t\) dollars and a \(\$2\) popcorn. They spend \(\$27\) in all. Write an equation and find the price of one ticket.
Problem 18: Taxi ride
A taxi charges $3.50 plus $2.25 for each mile. Aisha pays $14.75 for a ride. Write an equation and find the number of miles \(m\) she rides.
Problem 19: Warming up
At 6 a.m. the temperature is \(-3^{\circ}\text{F}\). It rises by \(2.5^{\circ}\text{F}\) each hour. After \(h\) hours it is \(12^{\circ}\text{F}\). Write an equation and find \(h\).
Problem 20: Diego's number
Diego thinks of a number, adds 6, and multiplies the result by 5. He gets 55. (a) Find the number with an arithmetic solution. (b) Write and solve an equation. (c) Explain how the two solutions are alike.
See every chapter on the Grade 7 math page.