x/2+5= x/3-8 — step-by-step solution

Let's solve in

ℝ

\frac{x}{2} + 5 = \frac{x}{3} - 8

Let's add fractions:

\frac{x}{2}

+ 5

- \frac{x}{3}

+ 8 = 0

ⓘ Start from

5

and move forward

8

on the number line:

5 + 8

13

■Like terms are grouped by adding their coefficients:

\frac{x}{2} - \frac{x}{3}

\frac{x}{6}

\frac{x}{6} + 13 = 0

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

\frac{x}{6} + 13

\frac{x + 13 \cdot 6}{6}

\frac{x + 13 \cdot 6}{6} = 0

ⓘ Multiplications are done before additions and subtractions:

13 \cdot 6

(10 + 3) \cdot 6

10 \cdot 6 + 3 \cdot 6

60 + 18

78

\frac{x + 78}{6} = 0

⇥Let's solve in

ℝ

x + 78 = 0

▶Solution found:

x = -78