Precalculus Examples

$\frac{x}{4} - \frac{5}{3} = \frac{3 x}{8}$

Step 1

Multiply both sides by $8$ .

$(\frac{x}{4} - \frac{5}{3}) \cdot 8 = \frac{3 x}{8} \cdot 8$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{x}{4} - \frac{5}{3}) \cdot 8$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{x}{4} \cdot 8 - \frac{5}{3} \cdot 8 = \frac{3 x}{8} \cdot 8$

Step 2.1.1.2

Cancel the common factor of $4$ .

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Step 2.1.1.2.1

Factor $4$ out of $8$ .

$\frac{x}{4} \cdot (4 (2)) - \frac{5}{3} \cdot 8 = \frac{3 x}{8} \cdot 8$

Step 2.1.1.2.2

Cancel the common factor.

$\frac{x}{4} \cdot (4 \cdot 2) - \frac{5}{3} \cdot 8 = \frac{3 x}{8} \cdot 8$

Step 2.1.1.2.3

Rewrite the expression.

$x \cdot 2 - \frac{5}{3} \cdot 8 = \frac{3 x}{8} \cdot 8$

Step 2.1.1.3

Multiply $- \frac{5}{3} \cdot 8$ .

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Step 2.1.1.3.1

Multiply $8$ by $- 1$ .

$x \cdot 2 - 8 (\frac{5}{3}) = \frac{3 x}{8} \cdot 8$

Step 2.1.1.3.2

Combine $- 8$ and $\frac{5}{3}$ .

$x \cdot 2 + \frac{- 8 \cdot 5}{3} = \frac{3 x}{8} \cdot 8$

Step 2.1.1.3.3

Multiply $- 8$ by $5$ .

$x \cdot 2 + \frac{- 40}{3} = \frac{3 x}{8} \cdot 8$

Step 2.1.1.4

Simplify each term.

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Step 2.1.1.4.1

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

$2 \cdot x + \frac{- 40}{3} = \frac{3 x}{8} \cdot 8$

Step 2.1.1.4.2

Move the negative in front of the fraction.

$2 x - \frac{40}{3} = \frac{3 x}{8} \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $8$ .

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Step 2.2.1.1

Cancel the common factor.

$2 x - \frac{40}{3} = \frac{3 x}{8} \cdot 8$

Step 2.2.1.2

Rewrite the expression.

$2 x - \frac{40}{3} = 3 x$

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 $3 x$ from both sides of the equation.

$2 x - \frac{40}{3} - 3 x = 0$

Step 3.1.2

Subtract $3 x$ from $2 x$ .

$- x - \frac{40}{3} = 0$

Step 3.2

Add $\frac{40}{3}$ to both sides of the equation.

$- x = \frac{40}{3}$

Step 3.3

Divide each term in $- x = \frac{40}{3}$ by $- 1$ and simplify.

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Step 3.3.1

Divide each term in $- x = \frac{40}{3}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\frac{40}{3}}{- 1}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\frac{40}{3}}{- 1}$

Step 3.3.2.2

Divide $x$ by $1$ .

$x = \frac{\frac{40}{3}}{- 1}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Move the negative one from the denominator of $\frac{\frac{40}{3}}{- 1}$ .

$x = - 1 \cdot \frac{40}{3}$

Step 3.3.3.2

Rewrite $- 1 \cdot \frac{40}{3}$ as $- \frac{40}{3}$ .

$x = - \frac{40}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{40}{3}$

Decimal Form:

$x = - 13.\overline{3}$

Mixed Number Form:

$x = - 13 \frac{1}{3}$