Question

3) |2x - 3| = 0;4) |6 - 5x| = 0;5) |х+ 1| + 5 = 3;6) |x + 5| - 2 = 7.​

Answer 1

Ответ:

1) |2-3|=0

2x-3=0

x=1,5

1). |6-5x|=0

6-5x=0

-5x=-6

x=1.2

3). x=шешімі жоқ

4). |x+5|-2=7

x1=-14

x2=4

Answer 2

To solve absolute value equations, we'll need to consider both the positive and negative cases for the expression inside the absolute value.

1. |2x - 3| = 0: The absolute value of any real number is always non-negative. It's only zero when the expression inside is zero.

   So, solve: 2x - 3 = 0 2x = 3 x = 1.5

2. |6 - 5x| = 0: Solve: 6 - 5x = 0 -5x = -6 x = 1.2

3. |x + 1| + 5 = 3: Subtract 5 from both sides: |x + 1| = -2

   Absolute value cannot be negative, so there are no solutions for this equation.

4. |x + 5| - 2 = 7: Add 2 to both sides: |x + 5| = 9

   Consider two cases: Case 1: x + 5 = 9 x = 4

   Case 2: -(x + 5) = 9 -x - 5 = 9 -x = 14 x = -14

So, the solutions are:

1. x = 1.5
2. x = 1.2
3. No solutions
4. x = 4, x = -14