Answer:
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
