Suppose you were a contestant on a game show where they gave you the answer and you had to think of the corresponding question. If the answer were, "
Guidance
Solving MultiStep Equations by Using the Distributive Property
When faced with an equation such as
Example A
Solve for
Solution: Apply the Distributive Property:
Apply the Addition Property of Equality:
Simplify:
Apply the Multiplication Property of Equality:
The solution is
Check: Does
Example B
Solve for
Solution:
Checking the answer:
Example C
Solve for
Solution:
Checking the answer:
Vocabulary
Distributive Property: For any real numbers
The Addition Property of Equality: For all real numbers
If
The Multiplication Property of Equality: For all real numbers
If
Guided Practice
Solve for
Solution:
Step 1: Apply the Distributive Property.
Step 2: Combine like terms.
Step 3: Isolate the variable and its coefficient by using the Addition Property.
Step 4: Isolate the variable by applying the Multiplication Property.
Step 5: Check your answer.
Substitute
Therefore,
Practice
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK12 Basic Algebra: MultiStep Equations (15:01)
Note that in the next video there IS an error. At one point the teacher says that 135/6 is in simplest form. There is a common factor of 3 in both numerator and denominator. 135/6 can be simplified by that factor of 3 to 45/2, or 22.5.
In 1 – 22, solve the equation.

3(x−1)−2(x+3)=0 
7(w+20)−w=5 
9(x−2)=3x+3 
2(5a−13)=27 
29(i+23)=25 
4(v+14)=352 
22=2(p+2) 
−(m+4)=−5 
48=4(n+4) 
65(v−35)=625  \begin{align*}10(b3)=100\end{align*}
 \begin{align*}6v + 6(4v+1)=6\end{align*}
 \begin{align*}46=4(3s+4)6\end{align*}
 \begin{align*}8(1+7m)+6=14\end{align*}
 \begin{align*}0=7(6+3k)\end{align*}
 \begin{align*}35=7(2x)\end{align*}
 \begin{align*}3(3a+1)7a=35\end{align*}
 \begin{align*}2 \left (n+ \frac{7}{3} \right )= \frac{14}{3}\end{align*}
 \begin{align*} \frac{59}{60} = \frac{1}{6} \left ( \frac{4}{3} r5 \right )\end{align*}
 \begin{align*}\frac{4y+3}{7} = 9\end{align*}
 \begin{align*}(c+3)2c(13c)=2\end{align*}
 \begin{align*}5m3[7(12m)]=0\end{align*}