Pre-Algebra Examples

$\frac{9}{5} \cdot (x + 7) = \frac{- 10}{4} \cdot (x + 4)$

Step 1

Simplify $\frac{9}{5} \cdot (x + 7)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{9}{5} \cdot (x + 7) = \frac{- 10}{4} \cdot (x + 4)$

Step 1.2

Simplify by adding zeros.

$\frac{9}{5} \cdot (x + 7) = \frac{- 10}{4} \cdot (x + 4)$

Step 1.3

Apply the distributive property.

$\frac{9}{5} x + \frac{9}{5} \cdot 7 = \frac{- 10}{4} \cdot (x + 4)$

Step 1.4

Combine $\frac{9}{5}$ and $x$ .

$\frac{9 x}{5} + \frac{9}{5} \cdot 7 = \frac{- 10}{4} \cdot (x + 4)$

Step 1.5

Multiply $\frac{9}{5} \cdot 7$ .

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Step 1.5.1

Combine $\frac{9}{5}$ and $7$ .

$\frac{9 x}{5} + \frac{9 \cdot 7}{5} = \frac{- 10}{4} \cdot (x + 4)$

Step 1.5.2

Multiply $9$ by $7$ .

$\frac{9 x}{5} + \frac{63}{5} = \frac{- 10}{4} \cdot (x + 4)$

Step 2

Simplify $\frac{- 10}{4} \cdot (x + 4)$ .

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Step 2.1

Simplify terms.

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Step 2.1.1

Cancel the common factor of $- 10$ and $4$ .

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Step 2.1.1.1

Factor $2$ out of $- 10$ .

$\frac{9 x}{5} + \frac{63}{5} = \frac{2 (- 5)}{4} \cdot (x + 4)$

Step 2.1.1.2

Cancel the common factors.

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Step 2.1.1.2.1

Factor $2$ out of $4$ .

$\frac{9 x}{5} + \frac{63}{5} = \frac{2 \cdot - 5}{2 \cdot 2} \cdot (x + 4)$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{9 x}{5} + \frac{63}{5} = \frac{2 \cdot - 5}{2 \cdot 2} \cdot (x + 4)$

Step 2.1.1.2.3

Rewrite the expression.

$\frac{9 x}{5} + \frac{63}{5} = \frac{- 5}{2} \cdot (x + 4)$

Step 2.1.2

Move the negative in front of the fraction.

$\frac{9 x}{5} + \frac{63}{5} = - \frac{5}{2} \cdot (x + 4)$

Step 2.1.3

Apply the distributive property.

$\frac{9 x}{5} + \frac{63}{5} = - \frac{5}{2} x - \frac{5}{2} \cdot 4$

Step 2.1.4

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

$\frac{9 x}{5} + \frac{63}{5} = - \frac{x \cdot 5}{2} - \frac{5}{2} \cdot 4$

Step 2.1.5

Cancel the common factor of $2$ .

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Step 2.1.5.1

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

$\frac{9 x}{5} + \frac{63}{5} = - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot 4$

Step 2.1.5.2

Factor $2$ out of $4$ .

$\frac{9 x}{5} + \frac{63}{5} = - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot (2 (2))$

Step 2.1.5.3

Cancel the common factor.

$\frac{9 x}{5} + \frac{63}{5} = - \frac{x \cdot 5}{2} + \frac{- 5}{2} \cdot (2 \cdot 2)$

Step 2.1.5.4

Rewrite the expression.

$\frac{9 x}{5} + \frac{63}{5} = - \frac{x \cdot 5}{2} - 5 \cdot 2$

Step 2.1.6

Multiply $- 5$ by $2$ .

$\frac{9 x}{5} + \frac{63}{5} = - \frac{x \cdot 5}{2} - 10$

Step 2.2

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

$\frac{9 x}{5} + \frac{63}{5} = - \frac{5 x}{2} - 10$

Step 3

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

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Step 3.1

Add $\frac{5 x}{2}$ to both sides of the equation.

$\frac{9 x}{5} + \frac{63}{5} + \frac{5 x}{2} = - 10$

Step 3.2

To write $\frac{9 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 x}{5} \cdot \frac{2}{2} + \frac{5 x}{2} + \frac{63}{5} = - 10$

Step 3.3

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

$\frac{9 x}{5} \cdot \frac{2}{2} + \frac{5 x}{2} \cdot \frac{5}{5} + \frac{63}{5} = - 10$

Step 3.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{9 x}{5}$ by $\frac{2}{2}$ .

$\frac{9 x \cdot 2}{5 \cdot 2} + \frac{5 x}{2} \cdot \frac{5}{5} + \frac{63}{5} = - 10$

Step 3.4.2

Multiply $5$ by $2$ .

$\frac{9 x \cdot 2}{10} + \frac{5 x}{2} \cdot \frac{5}{5} + \frac{63}{5} = - 10$

Step 3.4.3

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

$\frac{9 x \cdot 2}{10} + \frac{5 x \cdot 5}{2 \cdot 5} + \frac{63}{5} = - 10$

Step 3.4.4

Multiply $2$ by $5$ .

$\frac{9 x \cdot 2}{10} + \frac{5 x \cdot 5}{10} + \frac{63}{5} = - 10$

Step 3.5

Combine the numerators over the common denominator.

$\frac{9 x \cdot 2 + 5 x \cdot 5}{10} + \frac{63}{5} = - 10$

Step 3.6

Simplify each term.

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Step 3.6.1

Simplify the numerator.

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Step 3.6.1.1

Factor $x$ out of $9 x \cdot 2 + 5 x \cdot 5$ .

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Step 3.6.1.1.1

Factor $x$ out of $9 x \cdot 2$ .

$\frac{x (9 \cdot 2) + 5 x \cdot 5}{10} + \frac{63}{5} = - 10$

Step 3.6.1.1.2

Factor $x$ out of $5 x \cdot 5$ .

$\frac{x (9 \cdot 2) + x (5 \cdot 5)}{10} + \frac{63}{5} = - 10$

Step 3.6.1.1.3

Factor $x$ out of $x (9 \cdot 2) + x (5 \cdot 5)$ .

$\frac{x (9 \cdot 2 + 5 \cdot 5)}{10} + \frac{63}{5} = - 10$

Step 3.6.1.2

Multiply $9$ by $2$ .

$\frac{x (18 + 5 \cdot 5)}{10} + \frac{63}{5} = - 10$

Step 3.6.1.3

Multiply $5$ by $5$ .

$\frac{x (18 + 25)}{10} + \frac{63}{5} = - 10$

Step 3.6.1.4

Add $18$ and $25$ .

$\frac{x \cdot 43}{10} + \frac{63}{5} = - 10$

Step 3.6.2

Move $43$ to the left of $x$ .

$\frac{43 x}{10} + \frac{63}{5} = - 10$

Step 4

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

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Step 4.1

Subtract $\frac{63}{5}$ from both sides of the equation.

$\frac{43 x}{10} = - 10 - \frac{63}{5}$

Step 4.2

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{43 x}{10} = - 10 \cdot \frac{5}{5} - \frac{63}{5}$

Step 4.3

Combine $- 10$ and $\frac{5}{5}$ .

$\frac{43 x}{10} = \frac{- 10 \cdot 5}{5} - \frac{63}{5}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{43 x}{10} = \frac{- 10 \cdot 5 - 63}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 10$ by $5$ .

$\frac{43 x}{10} = \frac{- 50 - 63}{5}$

Step 4.5.2

Subtract $63$ from $- 50$ .

$\frac{43 x}{10} = \frac{- 113}{5}$

Step 4.6

Move the negative in front of the fraction.

$\frac{43 x}{10} = - \frac{113}{5}$

Step 5

Multiply both sides of the equation by $\frac{10}{43}$ .

$\frac{10}{43} \cdot \frac{43 x}{10} = \frac{10}{43} (- \frac{113}{5})$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{10}{43} \cdot \frac{43 x}{10}$ .

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Step 6.1.1.1

Cancel the common factor of $10$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{10}{43} \cdot \frac{43 x}{10} = \frac{10}{43} (- \frac{113}{5})$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{43} (43 x) = \frac{10}{43} (- \frac{113}{5})$

Step 6.1.1.2

Cancel the common factor of $43$ .

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Step 6.1.1.2.1

Factor $43$ out of $43 x$ .

$\frac{1}{43} (43 (x)) = \frac{10}{43} (- \frac{113}{5})$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{43} (43 x) = \frac{10}{43} (- \frac{113}{5})$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{10}{43} (- \frac{113}{5})$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{10}{43} (- \frac{113}{5})$ .

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Step 6.2.1.1

Cancel the common factor of $5$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{113}{5}$ into the numerator.

$x = \frac{10}{43} \cdot \frac{- 113}{5}$

Step 6.2.1.1.2

Factor $5$ out of $10$ .

$x = \frac{5 (2)}{43} \cdot \frac{- 113}{5}$

Step 6.2.1.1.3

Cancel the common factor.

$x = \frac{5 \cdot 2}{43} \cdot \frac{- 113}{5}$

Step 6.2.1.1.4

Rewrite the expression.

$x = \frac{2}{43} \cdot - 113$

Step 6.2.1.2

Combine $\frac{2}{43}$ and $- 113$ .

$x = \frac{2 \cdot - 113}{43}$

Step 6.2.1.3

Simplify the expression.

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Step 6.2.1.3.1

Multiply $2$ by $- 113$ .

$x = \frac{- 226}{43}$

Step 6.2.1.3.2

Move the negative in front of the fraction.

$x = - \frac{226}{43}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{226}{43}$

Decimal Form:

$x = - 5.25581395 \dots$

Mixed Number Form:

$x = - 5 \frac{11}{43}$