Question

А)|3х-13|=3Б)|х-4|=2В)|21х+1|=20Г)|2х-1|=3

Answer 1

Решение на фотографиях.

Answer 2

Let's solve each equation step by step:

A) |3x - 13| = 3

To remove the absolute value, we can split the equation into two cases:

Case 1: 3x - 13 = 3 Adding 13 to both sides: 3x = 16 Dividing by 3: x = 16/3

Case 2: -(3x - 13) = 3 Expanding the negative sign: -3x + 13 = 3 Subtracting 13 from both sides: -3x = -10 Dividing by -3 (or multiplying by -1/3): x = 10/3

So the solutions to the equation are x = 16/3 and x = 10/3.

B) |x - 4| = 2

Again, we'll consider two cases:

Case 1: x - 4 = 2 Adding 4 to both sides: x = 6

Case 2: -(x - 4) = 2 Expanding the negative sign: -x + 4 = 2 Subtracting 4 from both sides: -x = -2 Dividing by -1 (or multiplying by -1): x = 2

The solutions to the equation are x = 6 and x = 2.

C) |21x + 1| = 20

We'll proceed with two cases:

Case 1: 21x + 1 = 20 Subtracting 1 from both sides: 21x = 19 Dividing by 21: x = 19/21

Case 2: -(21x + 1) = 20 Expanding the negative sign: -21x - 1 = 20 Adding 1 to both sides: -21x = 21 Dividing by -21 (or multiplying by -1/21): x = -1

The solutions to the equation are x = 19/21 and x = -1.

D) |2x - 1| = 3

Considering the two cases:

Case 1: 2x - 1 = 3 Adding 1 to both sides: 2x = 4 Dividing by 2: x = 2

Case 2: -(2x - 1) = 3 Expanding the negative sign: -2x + 1 = 3 Subtracting 1 from both sides: -2x = 2 Dividing by -2 (or multiplying by -1/2): x = -1

The solutions to the equation are x = 2 and x = -1.

So the solutions for each equation are: A) x = 16/3 and x = 10/3 B) x = 6 and x = 2 C) x = 19/21 and x = -1 D) x = 2 and x = -1