Pre-Algebra Examples

$\frac{8}{9} \cdot (x + 10) = 1 \frac{3}{5} + x$

Step 1

Simplify the left side.

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Step 1.1

Simplify $\frac{8}{9} \cdot (x + 10)$ .

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Step 1.1.1

Apply the distributive property.

$\frac{8}{9} x + \frac{8}{9} \cdot 10 = 1 \frac{3}{5} + x$

Step 1.1.2

Combine $\frac{8}{9}$ and $x$ .

$\frac{8 x}{9} + \frac{8}{9} \cdot 10 = 1 \frac{3}{5} + x$

Step 1.1.3

Multiply $\frac{8}{9} \cdot 10$ .

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Step 1.1.3.1

Combine $\frac{8}{9}$ and $10$ .

$\frac{8 x}{9} + \frac{8 \cdot 10}{9} = 1 \frac{3}{5} + x$

Step 1.1.3.2

Multiply $8$ by $10$ .

$\frac{8 x}{9} + \frac{80}{9} = 1 \frac{3}{5} + x$

Step 2

Simplify the right side.

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Step 2.1

Convert $1 \frac{3}{5}$ to an improper fraction.

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Step 2.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{8 x}{9} + \frac{80}{9} = 1 + \frac{3}{5} + x$

Step 2.1.2

Add $1$ and $\frac{3}{5}$ .

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Step 2.1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{8 x}{9} + \frac{80}{9} = \frac{5}{5} + \frac{3}{5} + x$

Step 2.1.2.2

Combine the numerators over the common denominator.

$\frac{8 x}{9} + \frac{80}{9} = \frac{5 + 3}{5} + x$

Step 2.1.2.3

Add $5$ and $3$ .

$\frac{8 x}{9} + \frac{80}{9} = \frac{8}{5} + x$

Step 3

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

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Step 3.1

Subtract $x$ from both sides of the equation.

$\frac{8 x}{9} + \frac{80}{9} - x = \frac{8}{5}$

Step 3.2

To write $- x$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{8 x}{9} - x \cdot \frac{9}{9} + \frac{80}{9} = \frac{8}{5}$

Step 3.3

Combine $- x$ and $\frac{9}{9}$ .

$\frac{8 x}{9} + \frac{- x \cdot 9}{9} + \frac{80}{9} = \frac{8}{5}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{8 x - x \cdot 9}{9} + \frac{80}{9} = \frac{8}{5}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{8 x - x \cdot 9 + 80}{9} = \frac{8}{5}$

Step 3.6

Multiply $9$ by $- 1$ .

$\frac{8 x - 9 x + 80}{9} = \frac{8}{5}$

Step 3.7

Subtract $9 x$ from $8 x$ .

$\frac{- x + 80}{9} = \frac{8}{5}$

Step 3.8

Factor $- 1$ out of $- x$ .

$\frac{- (x) + 80}{9} = \frac{8}{5}$

Step 3.9

Rewrite $80$ as $- 1 (- 80)$ .

$\frac{- (x) - 1 (- 80)}{9} = \frac{8}{5}$

Step 3.10

Factor $- 1$ out of $- (x) - 1 (- 80)$ .

$\frac{- (x - 80)}{9} = \frac{8}{5}$

Step 3.11

Rewrite $- (x - 80)$ as $- 1 (x - 80)$ .

$\frac{- 1 (x - 80)}{9} = \frac{8}{5}$

Step 3.12

Move the negative in front of the fraction.

$- \frac{x - 80}{9} = \frac{8}{5}$

Step 4

Multiply both sides of the equation by $- 9$ .

$- 9 (- \frac{x - 80}{9}) = - 9 (\frac{8}{5})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 9 (- \frac{x - 80}{9})$ .

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Step 5.1.1.1

Cancel the common factor of $9$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{x - 80}{9}$ into the numerator.

$- 9 \frac{- (x - 80)}{9} = - 9 (\frac{8}{5})$

Step 5.1.1.1.2

Factor $9$ out of $- 9$ .

$9 (- 1) \frac{- (x - 80)}{9} = - 9 (\frac{8}{5})$

Step 5.1.1.1.3

Cancel the common factor.

$9 \cdot - 1 \frac{- (x - 80)}{9} = - 9 (\frac{8}{5})$

Step 5.1.1.1.4

Rewrite the expression.

$- - (x - 80) = - 9 (\frac{8}{5})$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (x - 80) = - 9 (\frac{8}{5})$

Step 5.1.1.2.2

Multiply $x - 80$ by $1$ .

$x - 80 = - 9 (\frac{8}{5})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- 9 (\frac{8}{5})$ .

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Step 5.2.1.1

Multiply $- 9 (\frac{8}{5})$ .

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Step 5.2.1.1.1

Combine $- 9$ and $\frac{8}{5}$ .

$x - 80 = \frac{- 9 \cdot 8}{5}$

Step 5.2.1.1.2

Multiply $- 9$ by $8$ .

$x - 80 = \frac{- 72}{5}$

Step 5.2.1.2

Move the negative in front of the fraction.

$x - 80 = - \frac{72}{5}$

Step 6

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

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Step 6.1

Add $80$ to both sides of the equation.

$x = - \frac{72}{5} + 80$

Step 6.2

To write $80$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - \frac{72}{5} + 80 \cdot \frac{5}{5}$

Step 6.3

Combine $80$ and $\frac{5}{5}$ .

$x = - \frac{72}{5} + \frac{80 \cdot 5}{5}$

Step 6.4

Combine the numerators over the common denominator.

$x = \frac{- 72 + 80 \cdot 5}{5}$

Step 6.5

Simplify the numerator.

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Step 6.5.1

Multiply $80$ by $5$ .

$x = \frac{- 72 + 400}{5}$

Step 6.5.2

Add $- 72$ and $400$ .

$x = \frac{328}{5}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{328}{5}$

Decimal Form:

$x = 65.6$

Mixed Number Form:

$x = 65 \frac{3}{5}$