Pre-Algebra Examples

$\frac{x - 18}{8} = \frac{x - 9}{12} + \frac{5}{24}$

Step 1

Multiply both sides by $8$ .

$\frac{x - 18}{8} \cdot 8 = (\frac{x - 9}{12} + \frac{5}{24}) \cdot 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $8$ .

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Step 2.1.1.1

Cancel the common factor.

$\frac{x - 18}{8} \cdot 8 = (\frac{x - 9}{12} + \frac{5}{24}) \cdot 8$

Step 2.1.1.2

Rewrite the expression.

$x - 18 = (\frac{x - 9}{12} + \frac{5}{24}) \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $(\frac{x - 9}{12} + \frac{5}{24}) \cdot 8$ .

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Step 2.2.1.1

To write $\frac{x - 9}{12}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x - 18 = (\frac{x - 9}{12} \cdot \frac{2}{2} + \frac{5}{24}) \cdot 8$

Step 2.2.1.2

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.2.1

Multiply $\frac{x - 9}{12}$ by $\frac{2}{2}$ .

$x - 18 = (\frac{(x - 9) \cdot 2}{12 \cdot 2} + \frac{5}{24}) \cdot 8$

Step 2.2.1.2.2

Multiply $12$ by $2$ .

$x - 18 = (\frac{(x - 9) \cdot 2}{24} + \frac{5}{24}) \cdot 8$

Step 2.2.1.3

Combine the numerators over the common denominator.

$x - 18 = \frac{(x - 9) \cdot 2 + 5}{24} \cdot 8$

Step 2.2.1.4

Simplify the numerator.

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Step 2.2.1.4.1

Apply the distributive property.

$x - 18 = \frac{x \cdot 2 - 9 \cdot 2 + 5}{24} \cdot 8$

Step 2.2.1.4.2

Move $2$ to the left of $x$ .

$x - 18 = \frac{2 \cdot x - 9 \cdot 2 + 5}{24} \cdot 8$

Step 2.2.1.4.3

Multiply $- 9$ by $2$ .

$x - 18 = \frac{2 \cdot x - 18 + 5}{24} \cdot 8$

Step 2.2.1.4.4

Add $- 18$ and $5$ .

$x - 18 = \frac{2 x - 13}{24} \cdot 8$

Step 2.2.1.5

Cancel the common factor of $8$ .

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Step 2.2.1.5.1

Factor $8$ out of $24$ .

$x - 18 = \frac{2 x - 13}{8 (3)} \cdot 8$

Step 2.2.1.5.2

Cancel the common factor.

$x - 18 = \frac{2 x - 13}{8 \cdot 3} \cdot 8$

Step 2.2.1.5.3

Rewrite the expression.

$x - 18 = \frac{2 x - 13}{3}$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $3$ .

$(x - 18) \cdot 3 = \frac{2 x - 13}{3} \cdot 3$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Simplify $(x - 18) \cdot 3$ .

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Step 3.2.1.1.1

Apply the distributive property.

$x \cdot 3 - 18 \cdot 3 = \frac{2 x - 13}{3} \cdot 3$

Step 3.2.1.1.2

Simplify the expression.

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Step 3.2.1.1.2.1

Move $3$ to the left of $x$ .

$3 \cdot x - 18 \cdot 3 = \frac{2 x - 13}{3} \cdot 3$

Step 3.2.1.1.2.2

Multiply $- 18$ by $3$ .

$3 x - 54 = \frac{2 x - 13}{3} \cdot 3$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Cancel the common factor.

$3 x - 54 = \frac{2 x - 13}{3} \cdot 3$

Step 3.2.2.1.2

Rewrite the expression.

$3 x - 54 = 2 x - 13$

Step 3.3

Solve for $x$ .

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Step 3.3.1

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

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Step 3.3.1.1

Subtract $2 x$ from both sides of the equation.

$3 x - 54 - 2 x = - 13$

Step 3.3.1.2

Subtract $2 x$ from $3 x$ .

$x - 54 = - 13$

Step 3.3.2

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

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Step 3.3.2.1

Add $54$ to both sides of the equation.

$x = - 13 + 54$

Step 3.3.2.2

Add $- 13$ and $54$ .

$x = 41$