Solving Linear Equations
Example 1
Solve: 3(2x  6) = 2(x + 4)  50.
Solution
Step 1 Remove parentheses.
Distribute 3 and distribute 2.
Step 2 On each side of the equation,
combine like terms.
Combine 8 and 50.
Step 3 Isolate the variable.
Add 18 to both sides.
Simplify.
Add 2x to both sides.
Simplify.
Divide both sides by 8. 
3(2x  6)
6x  18
6x  18
6x  18 + 18
6x
6x + 2x
8x

=  2(x + 4)  50
=  2x  8  50
=  2x  58
=  2x  58 + 18
=  2x  40
=  2x  40 + 2x
=  40

Simplify.
Step 4 Check the solution in the original
equation.
We leave the check to you.

x

= 5 
The solution is x = 5.
Note:
We can also solve
6x  18 =  2x  58
by first adding 2x to both sides:
6x  18 + 2x
8x  18
8x  18 + 18
8x
x 
=  2x  58 + 2x
=  58
=  58 + 18
=  40
= 5 
The solution of the previous example was a unique real number.
