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

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