Pre-Algebra Examples

$\frac{4}{- 8} \cdot (x + 9) = \frac{5}{- 10} \cdot (x - 6)$

Step 1

Simplify $\frac{4}{- 8} \cdot (x + 9)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{4}{- 8} \cdot (x + 9) = \frac{5}{- 10} \cdot (x - 6)$

Step 1.2

Simplify by adding zeros.

$\frac{4}{- 8} \cdot (x + 9) = \frac{5}{- 10} \cdot (x - 6)$

Step 1.3

Cancel the common factor of $4$ and $- 8$ .

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Step 1.3.1

Factor $4$ out of $4$ .

$\frac{4 (1)}{- 8} \cdot (x + 9) = \frac{5}{- 10} \cdot (x - 6)$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $4$ out of $- 8$ .

$\frac{4 \cdot 1}{4 \cdot - 2} \cdot (x + 9) = \frac{5}{- 10} \cdot (x - 6)$

Step 1.3.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 \cdot - 2} \cdot (x + 9) = \frac{5}{- 10} \cdot (x - 6)$

Step 1.3.2.3

Rewrite the expression.

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

Step 1.4

Move the negative in front of the fraction.

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

Step 1.5

Apply the distributive property.

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

Step 1.6

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

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

Step 1.7

Multiply $- \frac{1}{2} \cdot 9$ .

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Step 1.7.1

Multiply $9$ by $- 1$ .

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

Step 1.7.2

Combine $- 9$ and $\frac{1}{2}$ .

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

Step 1.8

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{9}{2} = \frac{5}{- 10} \cdot (x - 6)$

Step 2

Simplify $\frac{5}{- 10} \cdot (x - 6)$ .

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Step 2.1

Cancel the common factor of $5$ and $- 10$ .

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Step 2.1.1

Factor $5$ out of $5$ .

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

Step 2.1.2

Cancel the common factors.

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Step 2.1.2.1

Factor $5$ out of $- 10$ .

$- \frac{x}{2} - \frac{9}{2} = \frac{5 \cdot 1}{5 \cdot - 2} \cdot (x - 6)$

Step 2.1.2.2

Cancel the common factor.

$- \frac{x}{2} - \frac{9}{2} = \frac{5 \cdot 1}{5 \cdot - 2} \cdot (x - 6)$

Step 2.1.2.3

Rewrite the expression.

$- \frac{x}{2} - \frac{9}{2} = \frac{1}{- 2} \cdot (x - 6)$

Step 2.2

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{9}{2} = - \frac{1}{2} \cdot (x - 6)$

Step 2.3

Apply the distributive property.

$- \frac{x}{2} - \frac{9}{2} = - \frac{1}{2} x - \frac{1}{2} \cdot - 6$

Step 2.4

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

$- \frac{x}{2} - \frac{9}{2} = - \frac{x}{2} - \frac{1}{2} \cdot - 6$

Step 2.5

Cancel the common factor of $2$ .

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Step 2.5.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- \frac{x}{2} - \frac{9}{2} = - \frac{x}{2} + \frac{- 1}{2} \cdot - 6$

Step 2.5.2

Factor $2$ out of $- 6$ .

$- \frac{x}{2} - \frac{9}{2} = - \frac{x}{2} + \frac{- 1}{2} \cdot (2 (- 3))$

Step 2.5.3

Cancel the common factor.

$- \frac{x}{2} - \frac{9}{2} = - \frac{x}{2} + \frac{- 1}{2} \cdot (2 \cdot - 3)$

Step 2.5.4

Rewrite the expression.

$- \frac{x}{2} - \frac{9}{2} = - \frac{x}{2} - 1 \cdot - 3$

Step 2.6

Multiply $- 1$ by $- 3$ .

$- \frac{x}{2} - \frac{9}{2} = - \frac{x}{2} + 3$

Step 3

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

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Step 3.1

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

$- \frac{x}{2} - \frac{9}{2} + \frac{x}{2} = 3$

Step 3.2

Combine the opposite terms in $- \frac{x}{2} - \frac{9}{2} + \frac{x}{2}$ .

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Step 3.2.1

Add $- \frac{x}{2}$ and $\frac{x}{2}$ .

$0 - \frac{9}{2} = 3$

Step 3.2.2

Subtract $\frac{9}{2}$ from $0$ .

$- \frac{9}{2} = 3$

Step 4

Since $- \frac{9}{2} \neq 3$ , there are no solutions.

No solution