Question

1) |x^2-9|=16 2)|2x-3| >=5

Answer 1

1)|x^2-9|=16
x^2-9=16
x^2-9=-16
x=5
x=-5

2)|2x-3|=5
2x-3=5
2x-3=-5
x=-1
x=4

Answer 2

1) х^2=16
х^2=-16
Х=4
Х=-4
2) 2х-3>=5
2х-3>=-5
2х>=-5+3
2х>=-2
Х>=(-1;-бесконечности)

Answer 3

To solve the absolute value equations and inequality, we'll consider both the positive and negative cases of the absolute value expression. Remember that |a| = b has two solutions: a = b and a = -b.

1. |x^2 - 9| = 16

Positive case: x^2 - 9 = 16 x^2 = 16 + 9 x^2 = 25 x = ±√25 x = ±5

Negative case: -(x^2 - 9) = 16 -x^2 + 9 = 16 -x^2 = 16 - 9 -x^2 = 7 x^2 = -7 (No real solutions, as the square of any real number cannot be negative)

Therefore, the solutions to the equation are x = 5 and x = -5.

2. |2x - 3| >= 5

Positive case: 2x - 3 >= 5 2x >= 5 + 3 2x >= 8 x >= 4

Negative case: -(2x - 3) >= 5 -2x + 3 >= 5 -2x >= 5 - 3 -2x >= 2 x <= -1

Combine both cases:

x <= -1 or x >= 4

So, the solution to the inequality is x <= -1 or x >= 4.