Algebra Examples

$- 4 (u + 4) = 3 (u + 4) + 7$

Step 1

Simplify $- 4 (u + 4)$ .

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Rewrite.

$0 + 0 - 4 (u + 4) = 3 (u + 4) + 7$

Simplify by adding zeros.

$- 4 (u + 4) = 3 (u + 4) + 7$

Apply the distributive property.

$- 4 u - 4 \cdot 4 = 3 (u + 4) + 7$

Multiply $- 4$ by $4$ .

$- 4 u - 16 = 3 (u + 4) + 7$

Step 2

Simplify $3 (u + 4) + 7$ .

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Simplify each term.

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Apply the distributive property.

$- 4 u - 16 = 3 u + 3 \cdot 4 + 7$

Multiply $3$ by $4$ .

$- 4 u - 16 = 3 u + 12 + 7$

Add $12$ and $7$ .

$- 4 u - 16 = 3 u + 19$

Step 3

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

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Subtract $3 u$ from both sides of the equation.

$- 4 u - 16 - 3 u = 19$

Subtract $3 u$ from $- 4 u$ .

$- 7 u - 16 = 19$

Step 4

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

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Add $16$ to both sides of the equation.

$- 7 u = 19 + 16$

Add $19$ and $16$ .

$- 7 u = 35$

Step 5

Divide each term in $- 7 u = 35$ by $- 7$ and simplify.

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Divide each term in $- 7 u = 35$ by $- 7$ .

$\frac{- 7 u}{- 7} = \frac{35}{- 7}$

Simplify the left side.

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Cancel the common factor of $- 7$ .

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Cancel the common factor.

$\frac{- 7 u}{- 7} = \frac{35}{- 7}$

Divide $u$ by $1$ .

$u = \frac{35}{- 7}$

Simplify the right side.

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Divide $35$ by $- 7$ .

$u = - 5$