|(3x+5)/3 |=9 — step-by-step solution

1) Let's solve in

ℝ

| \frac{3 x + 5}{3} | = 9

ⓘ A fraction whose numerator is a sum splits term by term, (a + b)/c = a/c + b/c:

\frac{3 x + 5}{3}

x + \frac{5}{3}

| x + \frac{5}{3} | = 9

Since

9 \geq 0

| x + \frac{5}{3} | = 9

is equivalent to

x + \frac{5}{3} = 9

x + \frac{5}{3} = -9

2) Let's solve in

ℝ

x + \frac{5}{3} = 9

ⓘ We subtract

\frac{5}{3}

from both sides

x = 9 - \frac{5}{3}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

9 - \frac{5}{3}

\frac{3 \cdot 9 - 5}{3}

x = \frac{3 \cdot 9 - 5}{3}

ⓘ Multiplications are done before additions and subtractions:

3 \cdot 9

27

x = \frac{27 - 5}{3}

ⓘ The numerator and the denominator are computed before the division:

27 - 5

22

Solution obtained:

x = \frac{22}{3}

3) Let's solve in

ℝ

x + \frac{5}{3} = -9

ⓘ We subtract

\frac{5}{3}

from both sides

x = - 9 - \frac{5}{3}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

- 9 - \frac{5}{3}

\frac{3 \cdot (-9) - 5}{3}

x = \frac{3 \cdot (-9) - 5}{3}

ⓘ Multiplications are done before additions and subtractions. A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

3 \cdot (-9)

-27

x = \frac{- 27 - 5}{3}

ⓘ The numerator and the denominator are computed before the division:

- 27 - 5

-32

Solution found:

x = - \frac{32}{3}

▶Solution:

x = {- \frac{32}{3}, \frac{22}{3}}

4) The numeric value of:

x = {- \frac{32}{3}, \frac{22}{3}}

is:

▷

x = {\approx -10.6667, \approx 7.3333}