(7-5x)/3 =2x-8 — step-by-step solution

Let's solve in

ℝ

\frac{7 - 5 x}{3} = 2 x - 8

Let's sum the fractions:

\frac{7 - 5 x}{3} - 2 x + 8 = 0

ⅰ

\frac{7 - 5 x}{3} - 2 x

\frac{(7 - 5 x) + 3 \cdot (- 2 x)}{3}

\frac{(7 - 5 x) + 3 \cdot (- 2 x)}{3} + 8 = 0

ⓘ 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 (-2)

-6

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

\frac{7 - 5 x - 6 x}{3} + 8

\frac{(7 - 5 x - 6 x) + 8 \cdot 3}{3}

\frac{(7 - 5 x - 6 x) + 8 \cdot 3}{3} = 0

ⓘ Like terms are grouped by adding their coefficients:

- 5 x - 6 x

-11 x

■Multiplications are done before additions and subtractions:

8 \cdot 3

24

\frac{7 - 11 x + 24}{3} = 0

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

7 + 24

31

\frac{31 - 11 x}{3} = 0

⇥Let's solve in

ℝ

31 - 11 x = 0

⇥

11 x = 31

⇥ⓘ Both sides are divided by

11

▶Solution found:

x = \frac{31}{11}

The numeric value of:

x = \frac{31}{11}

is:

▷

x = \approx 2.8182