-|2x-5|-1=-2 — step-by-step solution

1) Let's solve in

ℝ

- | 2 x - 5 | - 1 = -2

ⓘ We add

1

to both sides

- | 2 x - 5 | = - 2 + 1

ⓘ Start from

-2

and move forward

1

on the number line, getting closer to zero:

- 2 + 1

-1

- | 2 x - 5 | = -1

Since

1 \geq 0

| 2 x - 5 | = 1

is equivalent to

2 x - 5 = 1

2 x - 5 = -1

2) Let's solve in

ℝ

2 x - 5 = 1

ⓘ We add

5

to both sides

2 x = 1 + 5

ⓘ Start from

1

and move forward

5

on the number line:

1 + 5

6

2 x = 6

ⓘ Both sides are divided by

2

x = \frac{6}{2}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{6}{2}

3

Solution found:

x = 3

3) Let's solve in

ℝ

2 x - 5 = -1

ⓘ We add

5

to both sides

2 x = - 1 + 5

ⓘ Start from

-1

and move forward

5

on the number line, going past zero:

- 1 + 5

4

2 x = 4

ⓘ Both sides are divided by

2

x = \frac{4}{2}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{4}{2}

2

Solution found:

x = 2

▶Solution:

x = {2, 3}