Basic Math Examples

$(- \frac{7}{5} u) + \frac{4}{5} = - u - \frac{1}{3}$

Step 1

Simplify each term.

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Step 1.1

Combine $u$ and $\frac{7}{5}$ .

$- \frac{u \cdot 7}{5} + \frac{4}{5} = - u - \frac{1}{3}$

Step 1.2

Move $7$ to the left of $u$ .

$- \frac{7 u}{5} + \frac{4}{5} = - u - \frac{1}{3}$

Step 2

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

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Step 2.1

Add $u$ to both sides of the equation.

$- \frac{7 u}{5} + \frac{4}{5} + u = - \frac{1}{3}$

Step 2.2

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

$- \frac{7 u}{5} + u \cdot \frac{5}{5} + \frac{4}{5} = - \frac{1}{3}$

Step 2.3

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

$- \frac{7 u}{5} + \frac{u \cdot 5}{5} + \frac{4}{5} = - \frac{1}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 7 u + u \cdot 5}{5} + \frac{4}{5} = - \frac{1}{3}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 7 u + u \cdot 5 + 4}{5} = - \frac{1}{3}$

Step 2.6

Move $5$ to the left of $u$ .

$\frac{- 7 u + 5 u + 4}{5} = - \frac{1}{3}$

Step 2.7

Add $- 7 u$ and $5 u$ .

$\frac{- 2 u + 4}{5} = - \frac{1}{3}$

Step 2.8

Factor $2$ out of $- 2 u + 4$ .

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Step 2.8.1

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

$\frac{2 (- u) + 4}{5} = - \frac{1}{3}$

Step 2.8.2

Factor $2$ out of $4$ .

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

Step 2.8.3

Factor $2$ out of $2 (- u) + 2 (2)$ .

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

Step 2.9

Factor $- 1$ out of $- u$ .

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

Step 2.10

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{2 (- (u) - 1 (- 2))}{5} = - \frac{1}{3}$

Step 2.11

Factor $- 1$ out of $- (u) - 1 (- 2)$ .

$\frac{2 (- (u - 2))}{5} = - \frac{1}{3}$

Step 2.12

Rewrite $- (u - 2)$ as $- 1 (u - 2)$ .

$\frac{2 (- 1 (u - 2))}{5} = - \frac{1}{3}$

Step 2.13

Move the negative in front of the fraction.

$- \frac{2 (u - 2)}{5} = - \frac{1}{3}$

Step 3

Multiply both sides of the equation by $- \frac{5}{2}$ .

$- \frac{5}{2} (- \frac{2 (u - 2)}{5}) = - \frac{5}{2} (- \frac{1}{3})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- \frac{5}{2} (- \frac{2 (u - 2)}{5})$ .

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$\frac{- 5}{2} (- \frac{2 (u - 2)}{5}) = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.1.2

Move the leading negative in $- \frac{2 (u - 2)}{5}$ into the numerator.

$\frac{- 5}{2} \cdot \frac{- 2 (u - 2)}{5} = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 (u - 2)}{5} = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 (u - 2)}{5} = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 (u - 2)) = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $- 2 (u - 2)$ .

$\frac{- 1}{2} (2 (- (u - 2))) = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- (u - 2))) = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.2.3

Rewrite the expression.

$- - (u - 2) = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 (u - 2) = - \frac{5}{2} (- \frac{1}{3})$

Step 4.1.1.3.2

Multiply $u - 2$ by $1$ .

$u - 2 = - \frac{5}{2} (- \frac{1}{3})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- \frac{5}{2} (- \frac{1}{3})$ .

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Step 4.2.1.1

Multiply $- 1$ by $- 1$ .

$u - 2 = 1 (\frac{5}{2}) \frac{1}{3}$

Step 4.2.1.2

Multiply $\frac{5}{2}$ by $1$ .

$u - 2 = \frac{5}{2} \cdot \frac{1}{3}$

Step 4.2.1.3

Multiply $\frac{5}{2}$ by $\frac{1}{3}$ .

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

Step 4.2.1.4

Multiply $2$ by $3$ .

$u - 2 = \frac{5}{6}$

Step 5

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

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Step 5.1

Add $2$ to both sides of the equation.

$u = \frac{5}{6} + 2$

Step 5.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$u = \frac{5}{6} + 2 \cdot \frac{6}{6}$

Step 5.3

Combine $2$ and $\frac{6}{6}$ .

$u = \frac{5}{6} + \frac{2 \cdot 6}{6}$

Step 5.4

Combine the numerators over the common denominator.

$u = \frac{5 + 2 \cdot 6}{6}$

Step 5.5

Simplify the numerator.

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Step 5.5.1

Multiply $2$ by $6$ .

$u = \frac{5 + 12}{6}$

Step 5.5.2

Add $5$ and $12$ .

$u = \frac{17}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$u = \frac{17}{6}$

Decimal Form:

$u = 2.8\overline{3}$

Mixed Number Form:

$u = 2 \frac{5}{6}$