# Answers to Questions on Equations And Inequalities

The answers to the questions on equations and inequalities with absolute value are presented.

### Question 1

Find all real solutions to the equation with absolute value.
2|-2x - 2| - 3 = 13

### Question 2

Find all real solutions to the equation with absolute value.
|x - 1| = 2x + 1

### Question 3

Find all real solutions to the equation with absolute value.
|2x - 1| = x2

answer a: -1 - √2 , -1 + √2 , 1

### Question 4

Find all real solutions to the equation with absolute value.
-2|x + 1| -2 = 4

### Question 5

Find all real solutions to the equation with absolute value.
|x - 1| = |x2 -2x + 1|

answer d: 0 , 1 , 2

### Question 6

Solve the inequality with absolute value..
|x - 1| >= 2

c: (-∞ , -1] U [3 , +∞)

### Question 7

Solve the inequality with absolute value..
-3|-2x + 4| <= 4

### Question 8

Solve the inequality with absolute value..
|3x + 1| <= 2x + 3

### Question 9

Solve the inequality with absolute value.
|x2 + x - 2| < x + 3

answer c: (-√5, -1) U (-1 , √5)

### Question 10

Solve the inequality with absolute values.
|x + 1| < |x2 + 2x + 2|