Pre-Algebra Examples

$\frac{x}{5} + x = - \frac{24}{5}$

Step 1

Simplify $\frac{x}{5} + x$ .

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Step 1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

Combine $x$ and $\frac{5}{5}$ .

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.3

Simplify the numerator.

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Step 1.3.1

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

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

Step 1.3.2

Add $x$ and $5 x$ .

$\frac{6 x}{5} = - \frac{24}{5}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$6 x = - 24$

Step 3

Divide each term in $6 x = - 24$ by $6$ and simplify.

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Step 3.1

Divide each term in $6 x = - 24$ by $6$ .

$\frac{6 x}{6} = \frac{- 24}{6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 24}{6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 24}{6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 24$ by $6$ .

$x = - 4$