-3x-4x=15+x/2 — step-by-step solution

1) Let's solve in

ℝ

- 3 x - 4 x = 15 + \frac{x}{2}

ⓘ Like terms are grouped by adding their coefficients:

- 3 x - 4 x

-7 x

-7 x = 15 + \frac{x}{2}

2) Let's sum the fractions:

- 7 x - 15 - \frac{x}{2} = 0

ⓘ Like terms are grouped by adding their coefficients:

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

\frac{-15 x}{2}

\frac{-15 x}{2} - 15 = 0

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

- \frac{15 x}{2} - 15

\frac{- 15 x - 15 \cdot 2}{2}

\frac{- 15 x - 15 \cdot 2}{2} = 0

ⓘ Multiplications are done before additions and subtractions:

15 \cdot 2

(10 + 5) \cdot 2

10 \cdot 2 + 5 \cdot 2

20 + 10

30

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

- 15 x - 30

- (15 x + 30)

- \frac{15 x + 30}{2} = 0

Let's solve in

ℝ

- (15 x + 30) = 0

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

- (15 x + 30)

- 15 x - 30

- 15 x - 30

- 15 x = 30

ⓘ Both sides are divided by

-15

x = \frac{30}{-15}

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

\frac{30}{-15}

- \frac{30}{15}

x = - \frac{30}{15}

The fraction:

\frac{30}{15}

simplifies by the common factor:

15

into the new expression:

2

▶Solution obtained:

x = -2