Algebra Examples

$- 5 (\frac{x}{15} - 16) - 30 = 50 - \frac{1}{3} x$

Step 1

Simplify $- 5 (\frac{x}{15} - 16) - 30$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$- 5 \frac{x}{15} - 5 \cdot - 16 - 30 = 50 - \frac{1}{3} x$

Step 1.1.2

Cancel the common factor of $5$ .

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Step 1.1.2.1

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{x}{15} - 5 \cdot - 16 - 30 = 50 - \frac{1}{3} x$

Step 1.1.2.2

Factor $5$ out of $15$ .

$5 \cdot - 1 \frac{x}{5 \cdot 3} - 5 \cdot - 16 - 30 = 50 - \frac{1}{3} x$

Step 1.1.2.3

Cancel the common factor.

$5 \cdot - 1 \frac{x}{5 \cdot 3} - 5 \cdot - 16 - 30 = 50 - \frac{1}{3} x$

Step 1.1.2.4

Rewrite the expression.

$- 1 \frac{x}{3} - 5 \cdot - 16 - 30 = 50 - \frac{1}{3} x$

Step 1.1.3

Multiply $- 5$ by $- 16$ .

$- 1 \frac{x}{3} + 80 - 30 = 50 - \frac{1}{3} x$

Step 1.1.4

Rewrite $- 1 \frac{x}{3}$ as $- \frac{x}{3}$ .

$- \frac{x}{3} + 80 - 30 = 50 - \frac{1}{3} x$

Step 1.2

Subtract $30$ from $80$ .

$- \frac{x}{3} + 50 = 50 - \frac{1}{3} x$

Step 2

Combine $x$ and $\frac{1}{3}$ .

$- \frac{x}{3} + 50 = 50 - \frac{x}{3}$

Step 3

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

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Step 3.1

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

$- \frac{x}{3} + 50 + \frac{x}{3} = 50$

Step 3.2

Combine the opposite terms in $- \frac{x}{3} + 50 + \frac{x}{3}$ .

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Step 3.2.1

Add $- \frac{x}{3}$ and $\frac{x}{3}$ .

$0 + 50 = 50$

Step 3.2.2

Add $0$ and $50$ .

$50 = 50$

Step 4

Since $50 = 50$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$