Question

1. |4х-2|=6 2. ||2х+3|-5|=3 3. |3х+5|>7

Answer 1

1.

$4x=2 \pm 6$

$x= \frac{1}{2} \pm \frac{3}{2}$

2.

$|2x+3|-5=\pm 3$

$|2x+3|=5 \pm 3$

а) $|2x+3|=8; \ 2x+3=\pm 8; 2x=\pm 8 -3; \ x=\pm4 -0.75$

б) $|2x+3|=2; \ 2x=\pm 2-3; \ x=\pm 1-1.5$

3. $(3x+12)(3x-2)>0$

$(x+4)(x-\frac{2}{3})>0$

$x\frac{2}{3}$

Answer 2

1. To solve the equation |4x - 2| = 6, we need to consider two cases: 4x - 2 = 6 or 4x - 2 = -6 Solving for x in each case, we get: x = 2 or x = -1 Therefore, the solutions to the equation are x = 2 and x = -1.

2. To solve the equation ||2x + 3| - 5| = 3, we also need to consider two cases: |2x + 3| - 5 = 3 or |2x + 3| - 5 = -3 Solving for |2x + 3| in each case, we get: |2x + 3| = 8 or |2x + 3| = 2 Solving for x in each case, we get: x = 5/2 or x = -11/2 or x = 1 or x = -2 Therefore, the solutions to the equation are x = 5/2, x = -11/2, x = 1, and x = -2.

3. To solve the inequality |3x + 5| > 7, we need to consider two cases: 3x + 5 > 7 or 3x + 5 < -7 Solving for x in each case, we get: x > 2 or x < -4/3 Therefore, the solution to the inequality is the set of all real numbers x such that x > 2 or x < -4/3. This can be written as (-∞, -4/3) ∪ (2, ∞).