Question

1) 4(x+8)-7(x-1)<12 2) 5x-2(x-4)>9x+23

Answer 1

1) 4( х + 8 ) - 7( х - 1 ) < 12
4х + 32 -7х + 7 < 12
- 3х < 12 - 39
- 3х < - 27
Х > 9
Ответ ( 9 ; + бесконечность )
2) 5х - 2( х - 4 ) > 9х + 23
5х - 2х + 8 > 9х + 23
- 2х - 9х > 23 - 8
- 11х > 15
Х < - 15/11
Х < - 1 4/11
Ответ ( - бесконечность ; - 1 4/11 )

Answer 2

Let's solve the given inequalities step by step:

1. 4(x + 8) - 7(x - 1) < 12

First, distribute the terms inside the parentheses: 4x + 32 - 7x + 7 < 12

Combine like terms: -3x + 39 < 12

Subtract 39 from both sides: -3x < 12 - 39 -3x < -27

Divide both sides by -3, remembering to flip the inequality when dividing by a negative number: x > -27 / -3 x > 9

Therefore, the solution to the inequality is x > 9.

2. 5x - 2(x - 4) > 9x + 23

First, distribute the terms inside the parentheses: 5x - 2x + 8 > 9x + 23

Combine like terms: 3x + 8 > 9x + 23

Subtract 3x from both sides: 8 > 6x + 23

Subtract 23 from both sides: -15 > 6x

Divide both sides by 6: -15 / 6 > x -2.5 > x

Therefore, the solution to the inequality is x < -2.5.

In summary:

1. The solution to 4(x + 8) - 7(x - 1) < 12 is x > 9.
2. The solution to 5x - 2(x - 4) > 9x + 23 is x < -2.5.