Pre-Algebra Examples

$47 \frac{1}{3} = x + 4 (- \frac{11}{4} x + 1)$

Step 1

Simplify the left side.

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Step 1.1

Convert $47 \frac{1}{3}$ to an improper fraction.

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Step 1.1.1

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

$47 + \frac{1}{3} = x + 4 (- \frac{11}{4} x + 1)$

Step 1.1.2

Add $47$ and $\frac{1}{3}$ .

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Step 1.1.2.1

To write $47$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$47 \cdot \frac{3}{3} + \frac{1}{3} = x + 4 (- \frac{11}{4} x + 1)$

Step 1.1.2.2

Combine $47$ and $\frac{3}{3}$ .

$\frac{47 \cdot 3}{3} + \frac{1}{3} = x + 4 (- \frac{11}{4} x + 1)$

Step 1.1.2.3

Combine the numerators over the common denominator.

$\frac{47 \cdot 3 + 1}{3} = x + 4 (- \frac{11}{4} x + 1)$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $47$ by $3$ .

$\frac{141 + 1}{3} = x + 4 (- \frac{11}{4} x + 1)$

Step 1.1.2.4.2

Add $141$ and $1$ .

$\frac{142}{3} = x + 4 (- \frac{11}{4} x + 1)$

Step 2

Simplify the right side.

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Step 2.1

Simplify $x + 4 (- \frac{11}{4} x + 1)$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Combine $x$ and $\frac{11}{4}$ .

$\frac{142}{3} = x + 4 (- \frac{x \cdot 11}{4} + 1)$

Step 2.1.1.1.2

Move $11$ to the left of $x$ .

$\frac{142}{3} = x + 4 (- \frac{11 x}{4} + 1)$

Step 2.1.1.2

Apply the distributive property.

$\frac{142}{3} = x + 4 (- \frac{11 x}{4}) + 4 \cdot 1$

Step 2.1.1.3

Cancel the common factor of $4$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{11 x}{4}$ into the numerator.

$\frac{142}{3} = x + 4 \frac{- 11 x}{4} + 4 \cdot 1$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{142}{3} = x + 4 \frac{- 11 x}{4} + 4 \cdot 1$

Step 2.1.1.3.3

Rewrite the expression.

$\frac{142}{3} = x - 11 x + 4 \cdot 1$

Step 2.1.1.4

Multiply $4$ by $1$ .

$\frac{142}{3} = x - 11 x + 4$

Step 2.1.2

Subtract $11 x$ from $x$ .

$\frac{142}{3} = - 10 x + 4$

Step 3

Rewrite the equation as $- 10 x + 4 = \frac{142}{3}$ .

$- 10 x + 4 = \frac{142}{3}$

Step 4

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

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Step 4.1

Subtract $4$ from both sides of the equation.

$- 10 x = \frac{142}{3} - 4$

Step 4.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- 10 x = \frac{142}{3} - 4 \cdot \frac{3}{3}$

Step 4.3

Combine $- 4$ and $\frac{3}{3}$ .

$- 10 x = \frac{142}{3} + \frac{- 4 \cdot 3}{3}$

Step 4.4

Combine the numerators over the common denominator.

$- 10 x = \frac{142 - 4 \cdot 3}{3}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 4$ by $3$ .

$- 10 x = \frac{142 - 12}{3}$

Step 4.5.2

Subtract $12$ from $142$ .

$- 10 x = \frac{130}{3}$

Step 5

Divide each term in $- 10 x = \frac{130}{3}$ by $- 10$ and simplify.

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Step 5.1

Divide each term in $- 10 x = \frac{130}{3}$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{\frac{130}{3}}{- 10}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 10$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{\frac{130}{3}}{- 10}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{130}{3}}{- 10}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{130}{3} \cdot \frac{1}{- 10}$

Step 5.3.2

Cancel the common factor of $10$ .

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Step 5.3.2.1

Factor $10$ out of $130$ .

$x = \frac{10 (13)}{3} \cdot \frac{1}{- 10}$

Step 5.3.2.2

Factor $10$ out of $- 10$ .

$x = \frac{10 \cdot 13}{3} \cdot \frac{1}{10 \cdot - 1}$

Step 5.3.2.3

Cancel the common factor.

$x = \frac{10 \cdot 13}{3} \cdot \frac{1}{10 \cdot - 1}$

Step 5.3.2.4

Rewrite the expression.

$x = \frac{13}{3} \cdot \frac{1}{- 1}$

Step 5.3.3

Multiply $\frac{13}{3}$ by $\frac{1}{- 1}$ .

$x = \frac{13}{3 \cdot - 1}$

Step 5.3.4

Simplify the expression.

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Step 5.3.4.1

Multiply $3$ by $- 1$ .

$x = \frac{13}{- 3}$

Step 5.3.4.2

Move the negative in front of the fraction.

$x = - \frac{13}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{13}{3}$

Decimal Form:

$x = - 4.\overline{3}$

Mixed Number Form:

$x = - 4 \frac{1}{3}$