Basic Math Examples

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

Step 1

Multiply both sides by $16$ .

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

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 $16$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Combine the numerators over the common denominator.

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

Step 2.2.1.2

Subtract $8$ from $5$ .

$x = \frac{x - 3}{8} \cdot 16$

Step 2.2.1.3

Cancel the common factor of $8$ .

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Step 2.2.1.3.1

Factor $8$ out of $16$ .

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

Step 2.2.1.3.2

Cancel the common factor.

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

Step 2.2.1.3.3

Rewrite the expression.

$x = (x - 3) \cdot 2$

Step 2.2.1.4

Apply the distributive property.

$x = x \cdot 2 - 3 \cdot 2$

Step 2.2.1.5

Simplify the expression.

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Step 2.2.1.5.1

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

$x = 2 \cdot x - 3 \cdot 2$

Step 2.2.1.5.2

Multiply $- 3$ by $2$ .

$x = 2 x - 6$

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 $2 x$ from both sides of the equation.

$x - 2 x = - 6$

Step 3.1.2

Subtract $2 x$ from $x$ .

$- x = - 6$

Step 3.2

Divide each term in $- x = - 6$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 6$ by $- 1$ .

$x = 6$