-2(5v-12)>6-v — step-by-step solution

Let's solve in

ℝ

-2 \cdot (5 v - 12) > 6 - v

ⓘ Expand by multiplying each term inside the parentheses:

- 2 \cdot (5 v - 12)

- (10 v - 24)

- (10 v - 24) > 6 - v

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

- (10 v - 24)

- 10 v + 24

- 10 v + 24 > 6 - v

ⓘ We gather the terms in

v

on the right and the other terms on the left

24 - 6 > - v + 10 v

ⓘ Start from

24

and move back

6

on the number line:

24 - 6

18

■Like terms are grouped by adding their coefficients:

- v + 10 v

9 v

18 > 9 v

ⓘ Both sides are divided by

9

v < \frac{18}{9}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

9

, their greatest common divisor:

\frac{18}{9}

2

▶Solution obtained:

v < 2