(3-x)/5 =2x-6 — step-by-step solution

Let's solve in

ℝ

\frac{3 - x}{5} = 2 x - 6

Let's add fractions:

\frac{3 - x}{5} - 2 x + 6 = 0

ⅰ

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

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

\frac{(3 - x) + 5 \cdot (- 2 x)}{5} + 6 = 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:

5 \cdot (-2)

-10

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

\frac{3 - x - 10 x}{5} + 6

\frac{(3 - x - 10 x) + 6 \cdot 5}{5}

\frac{(3 - x - 10 x) + 6 \cdot 5}{5} = 0

ⓘ Like terms are grouped by adding their coefficients:

- x - 10 x

-11 x

■Multiplications are done before additions and subtractions:

6 \cdot 5

30

\frac{3 - 11 x + 30}{5} = 0

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

3 + 30

33

\frac{33 - 11 x}{5} = 0

⇥Let's solve in

ℝ

33 - 11 x = 0

⇥

11 x = 33

⇥ⓘ Both sides are divided by

11

⇥

x = \frac{33}{11}

⇥We divide the numerator and denominator of

\frac{33}{11}

by the common factor:

11

, which gives the new expression:

3

▶Solution found:

x = 3