Question

| 2x - 3 | - 5 или ( x - 4 ) * ( x + 1 ) = 0

Answer 1

• | 2x - 3 | - 5=0

2х-3=5

2х=8

х=4

2х-3=-5

2х=-5+3

2х=-2

х=-1

• (x - 4)*(x+1)=0

х²+х-4х-4=0

х²-3х-4=0

д=9+16=25

√д=5

х1=3-5/2=-1

х2=4

Answer 2

To solve the inequality and equation you provided, let's break it down into two parts and find the solutions for each:

1. Solve the inequality |2x - 3| - 5: To solve this inequality, we'll consider two cases based on the sign of the expression inside the absolute value:

Case 1: (2x - 3) is positive or zero (i.e., 2x - 3 ≥ 0) |2x - 3| - 5 = (2x - 3) - 5 = 2x - 8

For this case, we have: 2x - 8 ≥ 0 Solving for x: 2x ≥ 8 x ≥ 4

Case 2: (2x - 3) is negative (i.e., 2x - 3 < 0) |2x - 3| - 5 = -(2x - 3) - 5 = -2x + 2

For this case, we have: -2x + 2 ≥ 0 Solving for x: -2x ≥ -2 x ≤ 1

So the solution for the inequality is: 1 ≤ x ≤ 4

2. Solve the equation (x - 4) * (x + 1) = 0: To find the solutions for this equation, we set each factor to zero and solve for x:

x - 4 = 0 => x = 4 x + 1 = 0 => x = -1

So the solutions for the equation are: x = 4 and x = -1.

Combining the solutions from both parts, the final solution for the given problem is: x = -1, 1 ≤ x ≤ 4.