Precalculus Examples

$(\frac{x + 4}{5}) = 5 (\frac{x + 4}{5}) - 4$

Step 1

Multiply both sides by $5$ .

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

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 $5$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

Cancel the common factor.

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

Step 2.2.1.1.2

Rewrite the expression.

$x + 4 = (x + 4 - 4) \cdot 5$

Step 2.2.1.2

Combine the opposite terms in $x + 4 - 4$ .

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Step 2.2.1.2.1

Subtract $4$ from $4$ .

$x + 4 = (x + 0) \cdot 5$

Step 2.2.1.2.2

Add $x$ and $0$ .

$x + 4 = x \cdot 5$

Step 2.2.1.3

Move $5$ to the left of $x$ .

$x + 4 = 5 x$

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 $5 x$ from both sides of the equation.

$x + 4 - 5 x = 0$

Step 3.1.2

Subtract $5 x$ from $x$ .

$- 4 x + 4 = 0$

Step 3.2

Subtract $4$ from both sides of the equation.

$- 4 x = - 4$

Step 3.3

Divide each term in $- 4 x = - 4$ by $- 4$ and simplify.

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Step 3.3.1

Divide each term in $- 4 x = - 4$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 4}{- 4}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 4$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 4}{- 4}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4}{- 4}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 4$ by $- 4$ .

$x = 1$