Question

How can one fourthx − 3 = one halfx + 8 be set up as a system of equations?

Answer 1

First, set each half of the equation equal to zero:

1/4x - 3 = 0
1/2x +8 = 0

Notice how I stacked the equations, lining up "like terms."

Multiply both equations by "4" to eliminate the fractions:

(4) 1/4x -3 = 0 --> x - 12 = 0
(4) 1/2x+8 = 0 --> 2x + 32 = 0

Add the equations equal: 3x + 20 = 0
Subtract 20 from both side - 20 -20
Simplify 3x = -20
Divide both sides by 3 3 3
Final answer: x = -20/3