|6x-5|+5=7 — step-by-step solution

1) Let's solve in

ℝ

| 6 x - 5 | + 5 = 7

ⓘ We subtract

5

from both sides

| 6 x - 5 | = 7 - 5

ⓘ Start from

7

and move back

5

on the number line:

7 - 5

2

| 6 x - 5 | = 2

Since

2 \geq 0

| 6 x - 5 | = 2

is equivalent to

6 x - 5 = 2

6 x - 5 = -2

2) Let's solve in

ℝ

6 x - 5 = 2

ⓘ We add

5

to both sides

6 x = 2 + 5

ⓘ Start from

2

and move forward

5

on the number line:

2 + 5

7

6 x = 7

ⓘ Both sides are divided by

6

Solution found:

x = \frac{7}{6}

3) Let's solve in

ℝ

6 x - 5 = -2

ⓘ We add

5

to both sides

6 x = - 2 + 5

ⓘ Start from

-2

and move forward

5

on the number line, going past zero:

- 2 + 5

3

6 x = 3

ⓘ Both sides are divided by

6

x = \frac{3}{6}

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

3

, their greatest common divisor:

\frac{3}{6}

\frac{1 \cdot 3}{2 \cdot 3}

\frac{1}{2}

Solution found:

x = \frac{1}{2}

▶Solution:

x = {\frac{1}{2}, \frac{7}{6}}

4) The numeric value of:

x = {\frac{1}{2}, \frac{7}{6}}

equals:

▷

x = {0.5, \approx 1.1667}