-4(v+4)=3(v+4)+7 — step-by-step solution

Let's solve in

ℝ

-4 \cdot (v + 4) = 3 \cdot (v + 4) + 7

ⓘ Expand by multiplying each term inside the parentheses:

- 4 \cdot (v + 4)

- (4 v + 16)

3 \cdot (v + 4)

3 v + 12

- (4 v + 16) = 3 v + 12 + 7

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

- (4 v + 16)

- 4 v - 16

■Start from

12

and move forward

7

on the number line:

12 + 7

19

- 4 v - 16 = 3 v + 19

ⓘ We gather the terms in

v

on the right and the other terms on the left

- 16 - 19 = 3 v + 4 v

ⓘ Start from

-16

and move back

19

more on the number line, away from zero:

- 16 - 19

-35

■Like terms are grouped by adding their coefficients:

3 v + 4 v

7 v

-35 = 7 v

ⓘ Both sides are divided by

7

v = - \frac{35}{7}

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

7

, their greatest common divisor:

- \frac{35}{7}

-5

▶Solution obtained:

v = -5