Twice a number decreased by 8 is 2 less than half the number

x = 4

"Translating" the sentence into numbers:

Twice a number → x * 2 or 2x

2x decreased by 8 → 2x - 8

2x - 8 is 2 less than half the number → 2x - 8 = x/2 - 2

Solving the equation:

2x - 8 = x/2 - 2

2x - 8 = 1/2x - 2

2x - 1/2x - 8 = -2

3/2x - 8 = -2

3/2x = -2 + 8

3/2x = 6

2/3x = 6 (!!)

x = 6 * 2/3

x = (6 * 2) / 3

x = 12 / 3

x = 4

(!!) → On that step what we must do is multiply both sides by 2/3 (which we obtain by flipping 3/2). But, since results would be the same, we just flipped the equation and followed a standard procedure.

Proving the equation:

2(4) - 8 = 4/2 - 2

8 - 8 = 4/2 - 2

0 = 4/2 - 2

0 = 2 - 2

0 = 0 → Both sides of the equation are equal. The equation is correct, 4 is the answer.

Hope it helped,

BiologiaMagister

77

step-by-step explanation: