x/3+3=2x+10 — step-by-step solution

1) Let's solve in

ℝ

\frac{x}{3} + 3 = 2 x + 10

2) Let's sum the fractions:

\frac{x}{3}

+ 3

- 2 x

- 10 = 0

ⓘ Start from

3

and move back

10

on the number line, going below zero:

3 - 10

-7

■Like terms are grouped by adding their coefficients:

\frac{x}{3} - 2 x

\frac{-5 x}{3}

\frac{-5 x}{3} - 7 = 0

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

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

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

\frac{- 5 x - 7 \cdot 3}{3} = 0

ⓘ Multiplications are done before additions and subtractions:

7 \cdot 3

21

■The minus sign is factored out, changing the sign of each term:

- 5 x - 21

- (5 x + 21)

- \frac{5 x + 21}{3} = 0

Let's solve in

ℝ

- (5 x + 21) = 0

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (5 x + 21)

- 5 x - 21

- 5 x - 21

- 5 x = 21

ⓘ Both sides are divided by

-5

x = \frac{21}{-5}

ⓘ The sign of a fraction goes in front of the bar, whether it comes from the numerator or the denominator:

\frac{21}{-5}

- \frac{21}{5}

▶Solution found:

x = - \frac{21}{5}

3) The numeric value of:

x = - \frac{21}{5}

is:

▷

x = -4.2