Solve for u 4(u+1)+5=6(u-1)+u

$4 (u + 1) + 5 = 6 (u - 1) + u$

Step 1

Since $u$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$6 (u - 1) + u = 4 (u + 1) + 5$

Step 2

Simplify $6 (u - 1) + u$ .

Simplify each term.

Apply the distributive property.

$6 u + 6 \cdot - 1 + u = 4 (u + 1) + 5$

Multiply $6$ by $- 1$ .

$6 u - 6 + u = 4 (u + 1) + 5$

Add $6 u$ and $u$ .

$7 u - 6 = 4 (u + 1) + 5$

Step 3

Simplify $4 (u + 1) + 5$ .

Simplify each term.

Apply the distributive property.

$7 u - 6 = 4 u + 4 \cdot 1 + 5$

Multiply $4$ by $1$ .

$7 u - 6 = 4 u + 4 + 5$

Add $4$ and $5$ .

$7 u - 6 = 4 u + 9$

Step 4

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

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

$7 u - 6 - 4 u = 9$

Subtract $4 u$ from $7 u$ .

$3 u - 6 = 9$

Step 5

Move all terms not containing $u$ to the right side of the equation.

Add $6$ to both sides of the equation.

$3 u = 9 + 6$

Add $9$ and $6$ .

$3 u = 15$

Step 6

Divide each term in $3 u = 15$ by $3$ and simplify.

Divide each term in $3 u = 15$ by $3$ .

$\frac{3 u}{3} = \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 u}{3} = \frac{15}{3}$

Divide $u$ by $1$ .

$u = \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$u = 5$

Solve for u 4(u+1)+5=6(u-1)+u

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