Solve for u 5(u+1)-u=4(u-1)+9

$5 (u + 1) - u = 4 (u - 1) + 9$

Step 1

Simplify $5 (u + 1) - u$ .

Simplify each term.

Apply the distributive property.

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

Multiply $5$ by $1$ .

$5 u + 5 - u = 4 (u - 1) + 9$

Subtract $u$ from $5 u$ .

$4 u + 5 = 4 (u - 1) + 9$

Step 2

Simplify $4 (u - 1) + 9$ .

Simplify each term.

Apply the distributive property.

$4 u + 5 = 4 u + 4 \cdot - 1 + 9$

Multiply $4$ by $- 1$ .

$4 u + 5 = 4 u - 4 + 9$

Add $- 4$ and $9$ .

$4 u + 5 = 4 u + 5$

Step 3

Move all terms containing $u$ to the left side of the equation.

Subtract $4 u$ from both sides of the equation.

$4 u + 5 - 4 u = 5$

Combine the opposite terms in $4 u + 5 - 4 u$ .

Subtract $4 u$ from $4 u$ .

$0 + 5 = 5$

Add $0$ and $5$ .

$5 = 5$

Step 4

Since $5 = 5$ , the equation will always be true for any value of $u$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$