|4x-1|=2 — step-by-step solution | Explain MAths

|4x-1|=2

1) Let's solve in

ℝ

:

| 4 x - 1 | = 2

Since

2 \geq 0

,

| 4 x - 1 | = 2

is equivalent to

4 x - 1 = 2

or

4 x - 1 = -2

2) Let's solve in

ℝ

:

4 x - 1 = 2

ⓘ We add

1

to both sides

4 x = 2 + 1

ⓘ Start from

2

and move forward

1

on the number line:

2 + 1

=

3

4 x = 3

ⓘ Both sides are divided by

4

Solution found:

x = \frac{3}{4}

3) Let's solve in

ℝ

:

4 x - 1 = -2

ⓘ We add

1

to both sides

4 x = - 2 + 1

ⓘ Start from

-2

and move forward

1

on the number line, getting closer to zero:

- 2 + 1

=

-1

4 x = -1

ⓘ Both sides are divided by

4

Solution obtained:

x = - \frac{1}{4}

▶Solution:

x = {- \frac{1}{4}, \frac{3}{4}}

4) The numeric value of:

x = {- \frac{1}{4}, \frac{3}{4}}

is:

▷

x = {-0.25, 0.75}