Algebra Examples

$- 2 u = \frac{4}{3} (3 u + 6) - 2 (3 + \frac{5}{2} u)$

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.

$\frac{4}{3} \cdot (3 u + 6) - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2

Simplify $\frac{4}{3} \cdot (3 u + 6) - 2 (3 + \frac{5}{2} u)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{4}{3} (3 u) + \frac{4}{3} \cdot 6 - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.2

Cancel the common factor of $3$ .

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Step 2.1.2.1

Factor $3$ out of $3 u$ .

$\frac{4}{3} (3 (u)) + \frac{4}{3} \cdot 6 - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.2.2

Cancel the common factor.

$\frac{4}{3} (3 u) + \frac{4}{3} \cdot 6 - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.2.3

Rewrite the expression.

$4 u + \frac{4}{3} \cdot 6 - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Factor $3$ out of $6$ .

$4 u + \frac{4}{3} \cdot (3 (2)) - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.3.2

Cancel the common factor.

$4 u + \frac{4}{3} \cdot (3 \cdot 2) - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.3.3

Rewrite the expression.

$4 u + 4 \cdot 2 - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.4

Multiply $4$ by $2$ .

$4 u + 8 - 2 (3 + \frac{5}{2} u) = - 2 u$

Step 2.1.5

Combine $\frac{5}{2}$ and $u$ .

$4 u + 8 - 2 (3 + \frac{5 u}{2}) = - 2 u$

Step 2.1.6

Apply the distributive property.

$4 u + 8 - 2 \cdot 3 - 2 \frac{5 u}{2} = - 2 u$

Step 2.1.7

Multiply $- 2$ by $3$ .

$4 u + 8 - 6 - 2 \frac{5 u}{2} = - 2 u$

Step 2.1.8

Cancel the common factor of $2$ .

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Step 2.1.8.1

Factor $2$ out of $- 2$ .

$4 u + 8 - 6 + 2 (- 1) \frac{5 u}{2} = - 2 u$

Step 2.1.8.2

Cancel the common factor.

$4 u + 8 - 6 + 2 \cdot - 1 \frac{5 u}{2} = - 2 u$

Step 2.1.8.3

Rewrite the expression.

$4 u + 8 - 6 - 1 (5 u) = - 2 u$

Step 2.1.9

Multiply $5$ by $- 1$ .

$4 u + 8 - 6 - 5 u = - 2 u$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $5 u$ from $4 u$ .

$- u + 8 - 6 = - 2 u$

Step 2.2.2

Subtract $6$ from $8$ .

$- u + 2 = - 2 u$

Step 3

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

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Step 3.1

Add $2 u$ to both sides of the equation.

$- u + 2 + 2 u = 0$

Step 3.2

Add $- u$ and $2 u$ .

$u + 2 = 0$

Step 4

Subtract $2$ from both sides of the equation.

$u = - 2$