Question

4(х-2)+2(х+3)=-10 |2х+8|=14 (х+4)(х+6)(х+7)=0 3.2у+1.5=1+1.6(2у+1)

Answer 1

1) 4 (х - 2) + 2 (х + 3)= -10;
4х - 8 + 2х + 6 = -10;
6х -2 = -10;
6х = -8;
х = -8/6;

2) |2х + 8| = 14;
|х + 4| = 7;
|х| + 4 = 7;
|х| = 3;
х1 = -3; х2 = 3;

3) (х + 4)(х + 6)(х + 7) = 0;
х + 4 = 0 , или х + 6 = 0, или х + 7 = 0;
х1 = -4; х2 = -6; х3 = -7;

4) 3.2у + 1.5 = 1 + 1.6 (2у + 1);
32у + 15 = 10 + 16 (2у + 1);
32у + 15 = 25 + 32у;
32у - 32у = 25 - 15;
0 = 10; ∅

Answer 2

Let's solve each equation step by step:

1. 4(x-2) + 2(x+3) = -10

First, distribute the terms: 4x - 8 + 2x + 6 = -10

Combine like terms: 6x - 2 = -10

Add 2 to both sides to isolate the variable term: 6x = -8

Now, divide both sides by 6 to solve for x: x = -8/6 x = -4/3

2. |2x + 8| = 14

We have an absolute value equation. It means we have to consider both the positive and negative solutions for the absolute value expression.

For the positive solution: 2x + 8 = 14

Subtract 8 from both sides: 2x = 6

Divide both sides by 2 to solve for x: x = 6/2 x = 3

For the negative solution: -(2x + 8) = 14

Distribute the negative sign: -2x - 8 = 14

Add 8 to both sides: -2x = 22

Divide both sides by -2 to solve for x: x = 22/-2 x = -11

So, we have two solutions for this equation: x = 3 and x = -11.

3. (x+4)(x+6)(x+7) = 0

To find the solutions, set each factor equal to zero and solve for x:

1. x + 4 = 0 x = -4

2. x + 6 = 0 x = -6

3. x + 7 = 0 x = -7

The solutions for this equation are x = -4, x = -6, and x = -7.

4. 3.2y + 1.5 = 1 + 1.6(2y + 1)

First, distribute the 1.6 on the right side: 3.2y + 1.5 = 1 + 3.2y + 1.6

Combine like terms: 3.2y + 1.5 = 4.2 + 3.2y

Subtract 3.2y from both sides to isolate the variable term: 1.5 = 4.2

This equation has no solutions since there is no value of y that satisfies the equation. It means there is no value of y that can make the equation true.