4(3+v)-v=6+3(v+2) — step-by-step solution

Let's solve in

ℝ

4 \cdot (3 + v) - v = 6 + 3 \cdot (v + 2)

4 \cdot (3 + v)

- v

- 6

- 3 \cdot (v + 2) = 0

ⓘ Expand by multiplying each term inside the parentheses:

4 \cdot (3 + v)

12 + 4 v

- 3 \cdot (v + 2)

- (3 v + 6)

12

+ 4 v

- v

- 6

- (3 v + 6) = 0

ⓘ Start from

12

and move back

6

on the number line:

12 - 6

6

■Like terms are grouped by adding their coefficients:

4 v - v

3 v

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

- (3 v + 6)

- 3 v - 6

6

+ 3 v

- 3 v

- 6 = 0

ⓘ Start from

6

and move back

6

on the number line, down to zero:

6 - 6

0

■Like terms are grouped by adding their coefficients:

3 v - 3 v

0

0 + 0 = 0

ⓘ Adding 0 changes nothing:

0 + 0

0

0 = 0

▶Solution obtained:

v \in ℝ