(2x)/5 =(3x)/4-14 — step-by-step solution

Let's solve in

ℝ

\frac{2 x}{5} = \frac{3 x}{4} - 14

Let's sum the fractions:

\frac{2 x}{5} - \frac{3 x}{4} + 14 = 0

ⓘ Like terms are grouped by adding their coefficients:

\frac{2 x}{5} - \frac{3 x}{4}

\frac{-7 x}{20}

\frac{-7 x}{20} + 14 = 0

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

- \frac{7 x}{20} + 14

\frac{- 7 x + 14 \cdot 20}{20}

\frac{- 7 x + 14 \cdot 20}{20} = 0

ⓘ Multiplications are done before additions and subtractions:

14 \cdot 20

(10 + 4) \cdot 20

10 \cdot 20 + 4 \cdot 20

200 + 80

280

\frac{- 7 x + 280}{20} = 0

⇥Let's solve in

ℝ

- 7 x + 280 = 0

⇥

7 x = 280

⇥ⓘ Both sides are divided by

7

⇥

x = \frac{280}{7}

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

7

, their greatest common divisor:

\frac{280}{7}

40

▶Solution found:

x = 40