Multi-Step Equations Practice Problems with Answers

If you master the skill of solving multi-step equations, it means you are now ready to tackle any topics in algebra that come your way.

For this exercise, I have prepared seven (7) multi-step equations for you to practice. If you feel the need to review the techniques involved in solving multi-step equations, take a short detour to review my other lesson about it. Click the link below to take you there!


1) Solve the multi-step equation for \large{c}.

c - 20 = 4 - 3c

Answer

Add both sides by 20. Next, add 3c to both sides. Finally, divide both sides by the coefficient of 4c which is 4 to get c=6.

c=6

2) Solve the multi-step equation for \large{n}.

- \,4\left( { - 3n - 8} \right) = 10n + 20

Answer
  • Remember to always perform the same operation on both sides of the equation.
  • Subtract by 32.
  • Subtract by 10n.
  • Divide by 2
  • The final solution is n=-6.
n=-6

3) Solve the multi-step equation for \large{y}.

2\left( {4 - y} \right) - 3\left( {y + 3} \right) = - 11

Answer

Apply twice the Distributive Property of Multiplication over Addition to the left side of the equation. Then combine like terms. Add both sides by 1 followed by dividing both sides of the equation by -5.

y=2

4) Solve the multi-step equation for \large{k}.

{\Large{{6k + 4} \over 2}} = 2k - 11

Answer

Multiply both sides by 2. Next, subtract 4 to both sides. Then, subtract 4k. Finally, divide by 2 to obtain the value of k which is -13.

k=-13

5) Solve the multi-step equation for \large{x}.

- \left( { - 8 - 3x} \right) = - 2\left( {1 - x} \right) + 6x

Answer

Apply the Distributive Property on both sides of the equation. Be careful when multiplying expressions with the same or different signs. Next, add 2 to both sides, then subtract 3x, and finally finish it off by dividing 5 to both sides.

2=x

6) Solve the multi-step equation for \large{m}.

{\large{3 \over 4}}m - 2\left( {m - 1} \right) = {\large{1 \over 4}}m + 5

Answer
m=-2

7) Solve the multi-step equation for \large{x}.

3\left( {3x - 8} \right) - 5\left( {3x - 8} \right) = 4\left( {x - 2} \right) - 6\left( {x - 2} \right)

Answer
x=3