|2x-1|=1 — step-by-step solution

1) Let's solve in

ℝ

| 2 x - 1 | = 1

Since

1 \geq 0

| 2 x - 1 | = 1

is equivalent to

2 x - 1 = 1

2 x - 1 = -1

2) Let's solve in

ℝ

2 x - 1 = 1

ⓘ We add

1

to both sides

2 x = 1 + 1

ⓘ Start from

1

and move forward

1

on the number line:

1 + 1

2

2 x = 2

ⓘ Both sides are divided by

2

x = \frac{2}{2}

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

2

, their greatest common divisor:

\frac{2}{2}

1

Solution found:

x = 1

3) Let's solve in

ℝ

2 x - 1 = -1

2 x - 1 + 1 = 0

ⓘ Start from

-1

and move forward

1

on the number line, up to zero:

- 1 + 1

0

2 x + 0 = 0

ⓘ Adding 0 changes nothing:

2 x + 0

2 x

2 x = 0

We simplify the expression by

2

⇥Let's solve in

ℝ

x = 0

⇥Solution found:

x = 0

▶Solution:

x = {0, 1}