Solving Linear Equations
To solve some equations, we must simplify the equation before using the
properties of equality.
Example 1
Simplifying the equations first
Solve the equation 2(x  4) + 5x = 34.
Solution
Before using the properties of equality, we simplify the expression on the
lefthand side of the equation:
2(x  4) + 5x 
= 34 

2x  8 + 5x 
= 34 
Distributive property 
7x  8 
= 34 
Combine like terms. 
7x  8 + 8 
= 34 + 8 
Add 8 to each side. 
7x 
= 42 
Simplify. 


Divide each side by 7 to get a single x on the left side.

x 
= 6 

To check, we replace x by 6 in the original equation and simplify:
2(6  4) + 5 Â· 6 
= 34 
2(2) + 30 
= 34 
34 
= 34 
The solution se to the equation is {6}.
