4(u+1)+u=5(u-1)+9 — step-by-step solution

Let's solve in

ℝ

4 \cdot (u + 1) + u = 5 \cdot (u - 1) + 9

4 \cdot (u + 1)

+ u

- 5 \cdot (u - 1)

- 9 = 0

ⓘ Expand by multiplying each term inside the parentheses:

4 \cdot (u + 1)

4 u + 4

- 5 \cdot (u - 1)

- (5 u - 5)

4 u

+ 4

+ u

- (5 u - 5)

- 9 = 0

ⓘ Like terms are grouped by adding their coefficients:

4 u + u

5 u

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

- (5 u - 5)

- 5 u + 5

5 u

+ 4

- 5 u

+ 5

- 9 = 0

ⓘ Start from

4

and move forward

5

on the number line:

4 + 5

9

■Like terms are grouped by adding their coefficients:

5 u - 5 u

0

0 + 9 - 9 = 0

ⓘ Adding 0 changes nothing:

0 + 9

9

■Start from

9

and move back

9

on the number line, down to zero:

9 - 9

0

0 = 0

▶Solution found:

u \in ℝ