2/3+x/5-1/4=4*x/5 — step-by-step solution

1) Let's solve in

ℝ

\frac{2}{3} + \frac{x}{5} - \frac{1}{4} = 4 \cdot \frac{x}{5}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

12

, the least common multiple of

3

and

4

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{2}{3} - \frac{1}{4}

\frac{2 \cdot 4}{3 \cdot 4} + \frac{-1 \cdot 3}{4 \cdot 3}

\frac{2 \cdot 4 - 1 \cdot 3}{3 \cdot 4}

■Multiplying a fraction by a number multiplies its numerator:

4 \cdot \frac{x}{5}

\frac{4 x}{5}

\frac{2 \cdot 4 - 1 \cdot 3}{3 \cdot 4} + \frac{x}{5} = \frac{4 x}{5}

ⓘ Multiplications are done before additions and subtractions:

2 \cdot 4

8

1 \cdot 3

3

ⅰ

3 \cdot 4

12

\frac{8 - 3}{12} + \frac{x}{5} = \frac{4 x}{5}

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

8 - 3

5

\frac{5}{12} + \frac{x}{5} = \frac{4 x}{5}

2) Let's sum the fractions:

\frac{5}{12} + \frac{x}{5} - \frac{4 x}{5} = 0

ⓘ Like terms are grouped by adding their coefficients:

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

\frac{-3 x}{5}

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

\frac{5}{12} + \frac{-3 x}{5}

\frac{5 \cdot 5 - 3 x \cdot 12}{12 \cdot 5}

\frac{5 \cdot 5 - 3 x \cdot 12}{12 \cdot 5} = 0

ⓘ Multiplications are done before additions and subtractions:

5 \cdot 5

25

3 \cdot 12

3 \cdot (10 + 2)

3 \cdot 10 + 3 \cdot 2

30 + 6

36

ⅰ

12 \cdot 5

(10 + 2) \cdot 5

10 \cdot 5 + 2 \cdot 5

50 + 10

60

\frac{25 - 36 x}{60} = 0

Let's solve in

ℝ

25 - 36 x = 0

36 x = 25

ⓘ Both sides are divided by

36

▶Solution found:

x = \frac{25}{36}

3) The numeric value of:

x = \frac{25}{36}

equals:

▷

x = \approx 0.6944