Practice Solving Two-Step Equations

1. Solve for $$p$$
   

   $$9(p-4)=-18$$

2. Solve for $$j$$
   

   $$\frac{j}{-2}+7=-12$$

3. Solve for $$k$$
   

   $$\frac{k}{4}+3=14$$

4. Solve for $$q$$
   

   $$3(q-7)=27$$

5. Solve for $$x$$
   

   $$-30=5(x+1)$$

6. Solve for $$b$$
   

   $$-11b+7=40$$

7. Solve for $$d$$
   

   $$41=12d-7$$

Source: Khan Academy, https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-2-step-equations-intro/e/linear_equations_2
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1. Let's divide and then add to get $$p$$ by itself.

   $$9(p-4)=-18$$
   $$\frac{9(p-4)}{9}=\frac{-18}{9}$$	divide each side by 9
   $$p-4=\frac{-18}{9}$$
   $$p-4=-2$$
   $$p-4+4=-2+4$$	add 4 to each side to get $$p$$ by itself
   $$p=2$$

   The answer:

   \(p=2\)

2. Let's subtract and then multiply to get \(j\) by itself.

   $$\frac{j}{-2}+7=-12$$
   $$\frac{j}{-2}+7-7=-12-7$$	subtract 7 from each side
   $$\frac{j}{-2}=-19$$
   $$\frac{j}{-2} \cdot -2 =-19 \cdot -2$$	multiply each side by -2 to get \(j\) by itself
   $$j =38$$

   
   

   The answer:

   \(j=38\)

3. Let's subtract and then multiply to get \(k\) by itself.

   $$\frac{k}{4}+3=14$$
   $$\frac{k}{4}+3-3=14-3$$	subtract 7 from each side
   $$\frac{k}{4}=11$$
   $$\frac{k}{4} \cdot 4=11\cdot 4$$	multiply each side by 4 to get \(k\) by itself
   $$k=44$$

   
   The answer:

   \(k=44\)

4. Let's divide and then add to get \(q\) by itself.

   $$3(q-7)=27$$
   $$\frac{3(q-7)}{3}=\frac{27}{3}$$	divide each side by 3
   $$q-7=9$$
   $$q-7+7=9+7$$	add 7 to each side to get \(q\) by itself
   $$q=16$$

   
   The answer:
   
   $$q=16$$
   

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

   $$-30=5(x+1)$$
   $$\frac{-30}{5}=\frac{5(x+1)}{5}$$	divide each side by 5
   $$-6=(x+1)$$
   $$-6-1=x+1-1$$	subtract 1 from each side to get $$x$$ by itself
   $$x=-7$$

   
   The answer:

   \(x=-7\)

6. Let's subtract and then divide to get \(b\) by itself.

   $$-11b+7=40$$
   $$-11b+7-7=40-7$$	subtract 7 from each side
   $$-11b=33$$
   $$\frac{-11b}{-11}=\frac{33}{-11}$$	divide each side by -11 to get \(b\) by itself
   $$b=-3$$

   
   

   The answer:

   \(b=-3\)

7. Let's add and then divide to get \(d\) by itself.

   $$41=12d-7$$
   $$41+7=12d-7+7$$	add 7 from each side
   $$48=12d$$
   $$\frac{48}{12} =\frac{12d}{12}$$	divide each side by 12 to get \(d\) by itself
   $$d=4$$

   
   The answer:

   \(d=4\)