Question

1. 2(x-4)=15 2. 4x+34=-(x-5) 3. 4x+34=-2(x-5) 4. (x-4):5=(2x-3):3

Answer 1

1) 2(х-4)=15

2х-8=15

2х=23

х=11,5

2) 4х+34=-(х-5)

4х+34=-х+5

4х+х=5-34

5х=-29

х=-5,8

3) 4х+34=-2(х-5)

4х+34=-2х+10

4х+2х=10-34

6х=-24

х=-4

4) (х-4)÷5=(2х-3)÷3

[Пропорционал]

3(х-4)=5(2х-3)

3х-12=10х-15

3х-10х=12-15

-7х=-3

х=3/7

Answer 2

Sure, let's solve each of these equations step by step:

1. $2(x - 4) = 15$

First, distribute the 2 on the left side:

$2x - 8 = 15$

Add 8 to both sides:

$2x = 23$

Divide by 2:

$x = 11.5$

2. $4x + 34 = -(x - 5)$

Distribute the negative sign on the right side:

$4x + 34 = -x + 5$

Add $x$ to both sides:

$5x + 34 = 5$

Subtract 34 from both sides:

$5x = -29$

Divide by 5:

$x = -5.8$

3. $4x + 34 = -2(x - 5)$

Distribute the $-2$ on the right side:

$4x + 34 = -2x + 10$

Add $2x$ to both sides:

$6x + 34 = 10$

Subtract 34 from both sides:

$6x = -24$

Divide by 6:

$x = -4$

4. $\frac{x - 4}{5} = \frac{2x - 3}{3}$

Cross-multiply to eliminate fractions:

$3(x - 4) = 5(2x - 3)$

Distribute on both sides:

$3x - 12 = 10x - 15$

Subtract $3x$ from both sides:

$-12 = 7x - 15$

Add 15 to both sides:

$3 = 7x$

Divide by 7:

$x = \frac{3}{7}$