2|3x-4|+7=9 — step-by-step solution

1) Let's solve in

ℝ

2 \cdot | 3 x - 4 | + 7 = 9

ⓘ We subtract

7

from both sides

2 \cdot | 3 x - 4 | = 9 - 7

ⓘ Start from

9

and move back

7

on the number line:

9 - 7

2

2 \cdot | 3 x - 4 | = 2

Since

2 \neq 0

, divide both sides by

2

| 3 x - 4 | = 1

Since

1 \geq 0

| 3 x - 4 | = 1

is equivalent to

3 x - 4 = 1

3 x - 4 = -1

2) Let's solve in

ℝ

3 x - 4 = 1

ⓘ We add

4

to both sides

3 x = 1 + 4

ⓘ Start from

1

and move forward

4

on the number line:

1 + 4

5

3 x = 5

ⓘ Both sides are divided by

3

Solution found:

x = \frac{5}{3}

3) Let's solve in

ℝ

3 x - 4 = -1

ⓘ We add

4

to both sides

3 x = - 1 + 4

ⓘ Start from

-1

and move forward

4

on the number line, going past zero:

- 1 + 4

3

3 x = 3

ⓘ Both sides are divided by

3

x = \frac{3}{3}

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

3

, their greatest common divisor:

\frac{3}{3}

1

Solution obtained:

x = 1

▶Solution:

x = {1, \frac{5}{3}}

4) The numeric value of:

x = {1, \frac{5}{3}}

equals:

▷

x = {1, \approx 1.6667}