Question

A) |3x|=12 Б) |х+2|=-2 В) |х-3|=8

Answer 1

Ответ:

І3хІ=12

х=+-4

Іх+2І=-2

Нету розвязков

Іх-3І=8

х=11 x=-5

Answer 2

To solve each of the absolute value equations, we'll isolate the absolute value expression and consider both the positive and negative cases.

A) |3x| = 12: We need to consider two cases: Case 1: 3x = 12 Solve for x: 3x = 12 x = 12 / 3 x = 4

Case 2: -(3x) = 12 Solve for x: -3x = 12 x = -12 / 3 x = -4

The solutions are x = 4 and x = -4.

B) |x + 2| = -2: The absolute value of any expression is always non-negative, so there are no real solutions in this case. Thus, the equation has no real solutions.

C) |x - 3| = 8: We need to consider two cases: Case 1: x - 3 = 8 Solve for x: x = 8 + 3 x = 11

Case 2: -(x - 3) = 8 Solve for x: -x + 3 = 8 -x = 8 - 3 -x = 5 x = -5

The solutions are x = 11 and x = -5.