Two-step equations

1. Solve for $p$.

$9(p−4)=−18$

2. Solve for $m$.

$13=2m+5$

3. Solve for $y$.

$6=2(y+2)$

4. Solve for $g$.

$3=\frac{g}{-4}-5$

5. Solve for $z$.

$42=−7(z−3)$

6. Solve for $d$.

$41=12d−7$

7. Solve for $q$.

$3(q−7)=27$

1. $p = 2$

Let's divide and then add to get $p$ by itself.

$9(p-4)=-18$

divide each side by $9$

$\begin{array}{r} \frac{9(p-4)}{9}=\frac{-18}{9} \\ \frac{g(p-4)}{9}=\frac{-18}{9} \\ p-4=\frac{-18}{9} \end{array}$

$p−4 = - 2$

add $4$ to each side to get $p$ by itself

$\begin{array}{r} p-4+4=-2+4 \\ p-4+4=-2+4 \\ p=-2+4 \end{array}$

The answer: $p = 2$

Let's check our work!

$\begin{array}{r} 9(p-4)=-18 \\ 9(2-4) \stackrel{?}{=}-18 \\ 9(-2) \stackrel{?}{=}-18 \\ -18=-18 \text { Yes! } \end{array}$

2. $m = 4$

Let's subtract and then divide to get $m$ by itself.

$13=2m+5$

subtract $5$ from each side

$\begin{aligned} &13-5=2 m+5-5 \\ &13-5=2 m+5-\not 5 \\ &13-5=2 m \end{aligned}$

$8 = 2m$

divide each side by $2$ to get $m$ by itself

$\begin{aligned} &\frac{8}{2}=\frac{2 m}{2} \\ &\frac{8}{2}=\frac{2 m}{2} \\ &\frac{8}{2}=m \end{aligned}$

The answer: $m = 4$

Let's check our work!

$\begin{aligned} &13=2 m+5 \\ &13 \stackrel{?}{=} 2(4)+5 \\ &13 \stackrel{?}{=} 8+5 \\ &13=13 \quad \text { Yes! } \end{aligned}$

3. $y = 1$

Let's divide and then subtract to get $y$ by itself.

$6=2(y+2)$

divide each side by $2$

$\begin{aligned} &\frac{6}{2}=\frac{2(y+2)}{2} \\ &\frac{6}{2}=\frac{2(y+2)}{2} \\ &\frac{6}{2}=y+2 \end{aligned}$

$3 = y +2$

subtract $2$ to get $y$ by itself

$\begin{aligned} &3-2=y+2-2 \\ &3-2=y+\not 2-2 \\ &3-2=y \end{aligned}$

The answer: $y = 1$

Let's check our work!

$\begin{aligned} &6=2(y+2) \\ &6 \stackrel{?}{=} 2(1+2) \\ &6 \stackrel{?}{=} 2(3) \\ &6=6 \quad \text { Yes! } \end{aligned}$

4. $g = -32$

Let's add and then multiply to get $g$ by itself.

$3=\frac{g}{-4}-5$

add $5$ to each side

$\begin{aligned} &3+5=\frac{g}{-4}-5+5 \\ &3+5=\frac{g}{-4}-5+5 \\ &3+5=\frac{g}{-4} \end{aligned}$

$8=\frac{g}{-4}$

multiply each side by −4 to get $g$ by itself

$8 \cdot-4=\frac{g}{-4} \cdot-4$

$8 \cdot-4=\frac{g}{-\not 4} \cdot -\not 4$

$8 \cdot-4=g$

Let's check our work!

$\begin{aligned} &3=\frac{g}{-4}-5 \\ &3 \stackrel{?}{=} \frac{-32}{-4}-5 \\ &3 \stackrel{?}{=} 8-5 \\ &3=3 \quad \text { Yes! } \end{aligned}$

5. $z = -3$

Let's divide and then add to get $z$ by itself.

$42=−7(z−3)$

divide each side by $−7$

$\begin{aligned} &\frac{42}{-7}=\frac{-7(z-3)}{-7} \\ &\frac{42}{-7}=\frac{7(z-3)}{-7} \\ &\frac{42}{-7}=z-3 \end{aligned}$

$-6 = z - 3$

add $3$ to each side to get $z$ by itself

$\begin{aligned} &-6+3=z-3+3 \\ &-6+3=z-\not 3+ \not 3 \\ &-6+3=z \end{aligned}$

The answer: $z = -3$

Let's check our work!

$\begin{aligned} &42=-7(z-3) \\ &42 \stackrel{?}{=}-7(-3-3) \\ &42 \stackrel{?}{=}-7(-6) \\ &42=42 \quad \text { Yes! } \end{aligned}$

6. $d = 4$

Let's add and then divide to get $d$ by itself.

$41=12d−7$

add $7$ to each side

$\begin{aligned} &41+7=12 d-7+7 \\ &41+7=12 d-\not 7+ \not 7 \\ &41+7=12 d \end{aligned}$

$48 = 12d$

$\begin{aligned} &\frac{48}{12}=\frac{12 d}{12} \\ &\frac{48}{12}=\frac{ \not {12} d}{\not {12}} \\ &\frac{48}{12}=d \end{aligned}$

The answer: $d = 4$

Let's check our work!

$\begin{aligned} &41=12 d-7 \\ &41 \stackrel{?}{=} 12(4)-7 \\ &41 \stackrel{?}{=} 48-7 \\ &41=41 \quad \text { Yes! } \end{aligned}$

7. $q = 16$

Let's divide and then add to get $q$ by itself.

$3(q−7)=27$

divide each side by $3$

$\begin{aligned} &\frac{3(q-7)}{3}=\frac{27}{3}\\ &\frac{\not 3(q-7)}{\not 3}=\frac{27}{3}\\ &q-7=\frac{27}{3} \end{aligned}$

$q - 7 = 9$

add $7$ to each side to get $q$ by itself

$\begin{array}{r} q-7+7=9+7 \\ q-7+7=9+7 \\ q=9+7 \end{array}$

The answer: $q = 16$

Let's check our work!

$\begin{aligned} 3(q-7) &=27 \\ 3(16-7) & \stackrel{?}{=} 27 \\ 3(9) & \stackrel{?}{=} 27 \\ 27 &=27 \quad \text { Yes! } \end{aligned}$