Multi-Step Equations Practice Problems with Answers

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 $\large{c}$.

$c - 20 = 4 - 3c$

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 $c=6$.

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

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

• 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 $n=-6$.

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

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

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 $-5$.

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

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

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 $-13$.

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

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

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.

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

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

7) Solve the multi-step equation for $\large{x}$.
$3\left( {3x - 8} \right) - 5\left( {3x - 8} \right) = 4\left( {x - 2} \right) - 6\left( {x - 2} \right)$