Question

|7x - 5| + 3 = 12; 2) 27 - 5|2x + 1| = - 3

Answer 1

Ответ:

1)7х-5+3=12

7х=12+5-3

7х=14

х=2

Ответ:2

2)27-10х-5=-3

-10х=-27+5-3

-10х=-25

х=2,5

Answer 2

To solve the equations, we'll start by isolating the absolute value expressions and then solve for the variable.

1. |7x - 5| + 3 = 12

Subtract 3 from both sides:

|7x - 5| = 12 - 3 |7x - 5| = 9

Now, we'll have two cases to consider:

Case 1: 7x - 5 is positive:

7x - 5 = 9

Add 5 to both sides:

7x = 9 + 5 7x = 14

Divide by 7:

x = 14 / 7 x = 2

Case 2: 7x - 5 is negative:

-(7x - 5) = 9

Distribute the negative sign:

-7x + 5 = 9

Subtract 5 from both sides:

-7x = 9 - 5 -7x = 4

Divide by -7:

x = 4 / -7 x ≈ -0.5714

So, the solutions to the first equation are x = 2 and x ≈ -0.5714.

2. 27 - 5|2x + 1| = -3

First, let's isolate the absolute value expression:

5|2x + 1| = 27 - (-3) 5|2x + 1| = 30

Now, we have two cases again:

Case 1: 2x + 1 is positive:

2x + 1 = 30 / 5 2x + 1 = 6

Subtract 1 from both sides:

2x = 6 - 1 2x = 5

Divide by 2:

x = 5 / 2 x = 2.5

Case 2: 2x + 1 is negative:

-(2x + 1) = 30 / 5 -2x - 1 = 6

Add 1 to both sides:

-2x = 6 + 1 -2x = 7

Divide by -2:

x = 7 / -2 x = -3.5

So, the solutions to the second equation are x = 2.5 and x = -3.5.

In summary:

1. The solutions to |7x - 5| + 3 = 12 are x = 2 and x ≈ -0.5714.
2. The solutions to 27 - 5|2x + 1| = -3 are x = 2.5 and x = -3.5.