Algebra Examples

$x + \frac{x + 5}{8} = \frac{x + 5}{16}$

Step 1

Multiply both sides by $16$ .

$(x + \frac{x + 5}{8}) \cdot 16 = \frac{x + 5}{16} \cdot 16$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(x + \frac{x + 5}{8}) \cdot 16$ .

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Step 2.1.1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(x \cdot \frac{8}{8} + \frac{x + 5}{8}) \cdot 16 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.2

Simplify terms.

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Step 2.1.1.2.1

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

$(\frac{x \cdot 8}{8} + \frac{x + 5}{8}) \cdot 16 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$\frac{x \cdot 8 + x + 5}{8} \cdot 16 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.3

Simplify the numerator.

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Step 2.1.1.3.1

Move $8$ to the left of $x$ .

$\frac{8 \cdot x + x + 5}{8} \cdot 16 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.3.2

Add $8 x$ and $x$ .

$\frac{9 x + 5}{8} \cdot 16 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.4

Simplify terms.

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Step 2.1.1.4.1

Cancel the common factor of $8$ .

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Step 2.1.1.4.1.1

Factor $8$ out of $16$ .

$\frac{9 x + 5}{8} \cdot (8 (2)) = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.4.1.2

Cancel the common factor.

$\frac{9 x + 5}{8} \cdot (8 \cdot 2) = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.4.1.3

Rewrite the expression.

$(9 x + 5) \cdot 2 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.4.2

Apply the distributive property.

$9 x \cdot 2 + 5 \cdot 2 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.4.3

Multiply.

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Step 2.1.1.4.3.1

Multiply $2$ by $9$ .

$18 x + 5 \cdot 2 = \frac{x + 5}{16} \cdot 16$

Step 2.1.1.4.3.2

Multiply $5$ by $2$ .

$18 x + 10 = \frac{x + 5}{16} \cdot 16$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $16$ .

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Step 2.2.1.1

Cancel the common factor.

$18 x + 10 = \frac{x + 5}{16} \cdot 16$

Step 2.2.1.2

Rewrite the expression.

$18 x + 10 = x + 5$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$18 x + 10 - x = 5$

Step 3.1.2

Subtract $x$ from $18 x$ .

$17 x + 10 = 5$

Step 3.2

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

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Step 3.2.1

Subtract $10$ from both sides of the equation.

$17 x = 5 - 10$

Step 3.2.2

Subtract $10$ from $5$ .

$17 x = - 5$

Step 3.3

Divide each term in $17 x = - 5$ by $17$ and simplify.

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Step 3.3.1

Divide each term in $17 x = - 5$ by $17$ .

$\frac{17 x}{17} = \frac{- 5}{17}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $17$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{17 x}{17} = \frac{- 5}{17}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 5}{17}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative in front of the fraction.

$x = - \frac{5}{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{5}{17}$

Decimal Form:

$x = - 0.29411764 \dots$