-6(v+1)=2(1-3v)-7 — step-by-step solution

Let's solve in

ℝ

-6 \cdot (v + 1) = 2 \cdot (1 - 3 v) - 7

- 6 \cdot (v + 1) - 2 \cdot (1 - 3 v) + 7 = 0

ⓘ Expand by multiplying each term inside the parentheses:

- 6 \cdot (v + 1)

- (6 v + 6)

- 2 \cdot (1 - 3 v)

- (2 - 6 v)

- (6 v + 6) - (2 - 6 v) + 7 = 0

- 6 v

- 6

- 2

+ 6 v

+ 7 = 0

ⓘ Start from

-6

and move back

2

more on the number line, away from zero:

- 6 - 2

-8

■Like terms are grouped by adding their coefficients:

- 6 v + 6 v

0

0 - 8 + 7 = 0

ⓘ Adding 0 changes nothing:

0 - 8

-8

■Start from

-8

and move forward

7

on the number line, getting closer to zero:

- 8 + 7

-1

-1 = 0

The statement

-1 = 0

is false, whatever the value of

v

▶Solution:

v \in \emptyset