Example 1: Solve
4(x + 2) - 2x = 2(x + 3)
According to our order of operations, what do we do first?
Work on the parentheses.
How do we do that here?
Distribute the multiplication.
Do it.
4x + 8 - 2x = 2x + 6
Collect the like terms on the left.
2x + 8 = 2x - 6
Subtract 2x from both sides.
2x + 8 - 2x = 2x + 6 - 2x, or
8
What can we conclude?
Since 8
¹ 6, there is no value of x which solves the original equation.Example 2: Solve
How do we handle the fractions?
We need the Least Common Denominator, the LCD.
What is the LCD here?
LCD = 12
How do we "clear the denominators"?
Multiply both sides by the LCD.
Set this up.
Distribute the 12.
Do the multiplication.
y*4 - 3*(2 - 3y) = 96
Distribute the -3.
Collect like terms.
13y - 6 = 96
Add 6 to both sides to isolate 13y.
13y = 96 + 6 = 102
Divide by 13 on both sides.
Let's check this with a calculator. First set up the original equation with this value of y.
Evaluate this.
Here is a list of keystrokes:
102,
(,2,-,3,*,102,¸ ,13,),¸ ,4,ENTER
It checks!