Algebra Examples

$\frac{3}{5} (\frac{1}{2} u + 6 - 5 u) = \frac{9}{10} u$

Step 1

Simplify $\frac{3}{5} \cdot (\frac{1}{2} u + 6 - 5 u)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{5} \cdot (\frac{1}{2} u + 6 - 5 u) = \frac{9}{10} u$

Step 1.2

Simplify by adding zeros.

$\frac{3}{5} \cdot (\frac{1}{2} u + 6 - 5 u) = \frac{9}{10} u$

Step 1.3

Combine $\frac{1}{2}$ and $u$ .

$\frac{3}{5} \cdot (\frac{u}{2} + 6 - 5 u) = \frac{9}{10} u$

Step 1.4

To write $- 5 u$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3}{5} \cdot (\frac{u}{2} - 5 u \cdot \frac{2}{2} + 6) = \frac{9}{10} u$

Step 1.5

Simplify terms.

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Step 1.5.1

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

$\frac{3}{5} \cdot (\frac{u}{2} + \frac{- 5 u \cdot 2}{2} + 6) = \frac{9}{10} u$

Step 1.5.2

Combine the numerators over the common denominator.

$\frac{3}{5} \cdot (\frac{u - 5 u \cdot 2}{2} + 6) = \frac{9}{10} u$

Step 1.6

Simplify each term.

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Step 1.6.1

Simplify the numerator.

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Step 1.6.1.1

Factor $u$ out of $u - 5 u \cdot 2$ .

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Step 1.6.1.1.1

Raise $u$ to the power of $1$ .

$\frac{3}{5} \cdot (\frac{u^{1} - 5 u \cdot 2}{2} + 6) = \frac{9}{10} u$

Step 1.6.1.1.2

Factor $u$ out of $u^{1}$ .

$\frac{3}{5} \cdot (\frac{u \cdot 1 - 5 u \cdot 2}{2} + 6) = \frac{9}{10} u$

Step 1.6.1.1.3

Factor $u$ out of $- 5 u \cdot 2$ .

$\frac{3}{5} \cdot (\frac{u \cdot 1 + u (- 5 \cdot 2)}{2} + 6) = \frac{9}{10} u$

Step 1.6.1.1.4

Factor $u$ out of $u \cdot 1 + u (- 5 \cdot 2)$ .

$\frac{3}{5} \cdot (\frac{u (1 - 5 \cdot 2)}{2} + 6) = \frac{9}{10} u$

Step 1.6.1.2

Multiply $- 5$ by $2$ .

$\frac{3}{5} \cdot (\frac{u (1 - 10)}{2} + 6) = \frac{9}{10} u$

Step 1.6.1.3

Subtract $10$ from $1$ .

$\frac{3}{5} \cdot (\frac{u \cdot - 9}{2} + 6) = \frac{9}{10} u$

Step 1.6.2

Move $- 9$ to the left of $u$ .

$\frac{3}{5} \cdot (\frac{- 9 \cdot u}{2} + 6) = \frac{9}{10} u$

Step 1.6.3

Move the negative in front of the fraction.

$\frac{3}{5} \cdot (- \frac{9 u}{2} + 6) = \frac{9}{10} u$

Step 1.7

Apply the distributive property.

$\frac{3}{5} (- \frac{9 u}{2}) + \frac{3}{5} \cdot 6 = \frac{9}{10} u$

Step 1.8

Multiply $\frac{3}{5} (- \frac{9 u}{2})$ .

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Step 1.8.1

Multiply $\frac{3}{5}$ by $\frac{9 u}{2}$ .

$- \frac{3 (9 u)}{5 \cdot 2} + \frac{3}{5} \cdot 6 = \frac{9}{10} u$

Step 1.8.2

Multiply $9$ by $3$ .

$- \frac{27 u}{5 \cdot 2} + \frac{3}{5} \cdot 6 = \frac{9}{10} u$

Step 1.8.3

Multiply $5$ by $2$ .

$- \frac{27 u}{10} + \frac{3}{5} \cdot 6 = \frac{9}{10} u$

Step 1.9

Multiply $\frac{3}{5} \cdot 6$ .

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Step 1.9.1

Combine $\frac{3}{5}$ and $6$ .

$- \frac{27 u}{10} + \frac{3 \cdot 6}{5} = \frac{9}{10} u$

Step 1.9.2

Multiply $3$ by $6$ .

$- \frac{27 u}{10} + \frac{18}{5} = \frac{9}{10} u$

Step 2

Combine $\frac{9}{10}$ and $u$ .

$- \frac{27 u}{10} + \frac{18}{5} = \frac{9 u}{10}$

Step 3

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

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Step 3.1

Subtract $\frac{9 u}{10}$ from both sides of the equation.

$- \frac{27 u}{10} + \frac{18}{5} - \frac{9 u}{10} = 0$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 27 u - 9 u}{10} + \frac{18}{5} = 0$

Step 3.3

Subtract $9 u$ from $- 27 u$ .

$\frac{- 36 u}{10} + \frac{18}{5} = 0$

Step 3.4

Simplify each term.

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Step 3.4.1

Cancel the common factor of $- 36$ and $10$ .

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Step 3.4.1.1

Factor $2$ out of $- 36 u$ .

$\frac{2 (- 18 u)}{10} + \frac{18}{5} = 0$

Step 3.4.1.2

Cancel the common factors.

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Step 3.4.1.2.1

Factor $2$ out of $10$ .

$\frac{2 (- 18 u)}{2 (5)} + \frac{18}{5} = 0$

Step 3.4.1.2.2

Cancel the common factor.

$\frac{2 (- 18 u)}{2 \cdot 5} + \frac{18}{5} = 0$

Step 3.4.1.2.3

Rewrite the expression.

$\frac{- 18 u}{5} + \frac{18}{5} = 0$

Step 3.4.2

Move the negative in front of the fraction.

$- \frac{18 u}{5} + \frac{18}{5} = 0$

Step 4

Subtract $\frac{18}{5}$ from both sides of the equation.

$- \frac{18 u}{5} = - \frac{18}{5}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 18 u = - 18$

Step 6

Divide each term in $- 18 u = - 18$ by $- 18$ and simplify.

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Step 6.1

Divide each term in $- 18 u = - 18$ by $- 18$ .

$\frac{- 18 u}{- 18} = \frac{- 18}{- 18}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 18$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 18 u}{- 18} = \frac{- 18}{- 18}$

Step 6.2.1.2

Divide $u$ by $1$ .

$u = \frac{- 18}{- 18}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $- 18$ by $- 18$ .

$u = 1$