3(3u+2)+5=2(2u-2) — step-by-step solution

Let's solve in

ℝ

3 \cdot (3 u + 2) + 5 = 2 \cdot (2 u - 2)

ⓘ Expand by multiplying each term inside the parentheses:

3 \cdot (3 u + 2)

9 u + 6

2 \cdot (2 u - 2)

4 u - 4

9 u + 6 + 5 = 4 u - 4

ⓘ Start from

6

and move forward

5

on the number line:

6 + 5

11

9 u + 11 = 4 u - 4

ⓘ We subtract

11

from both sides■Start from

-4

and move back

11

more on the number line, away from zero:

- 4 - 11

-15

9 u = 4 u - 15

ⓘ We subtract

4 u

from both sides

9 u - 4 u = -15

ⓘ Like terms are grouped by adding their coefficients:

9 u - 4 u

5 u

5 u = -15

ⓘ Both sides are divided by

5

u = - \frac{15}{5}

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

5

, their greatest common divisor:

- \frac{15}{5}

-3

▶Solution found:

u = -3