Pre-Algebra Examples

$- \frac{75 x}{4} > \frac{225}{2}$

Step 1

Divide each term in $- \frac{75 x}{4} > \frac{225}{2}$ by $- 1$ and simplify.

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Step 1.1

Divide each term in $- \frac{75 x}{4} > \frac{225}{2}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{75 x}{4}}{- 1} < \frac{\frac{225}{2}}{- 1}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{75 x}{4}}{1} < \frac{\frac{225}{2}}{- 1}$

Step 1.2.2

Divide $\frac{75 x}{4}$ by $1$ .

$\frac{75 x}{4} < \frac{\frac{225}{2}}{- 1}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative one from the denominator of $\frac{\frac{225}{2}}{- 1}$ .

$\frac{75 x}{4} < - 1 \cdot \frac{225}{2}$

Step 1.3.2

Rewrite $- 1 \cdot \frac{225}{2}$ as $- \frac{225}{2}$ .

$\frac{75 x}{4} < - \frac{225}{2}$

Step 2

Multiply both sides by $4$ .

$\frac{75 x}{4} \cdot 4 < - \frac{225}{2} \cdot 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{75 x}{4} \cdot 4 < - \frac{225}{2} \cdot 4$

Step 3.1.1.2

Rewrite the expression.

$75 x < - \frac{225}{2} \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- \frac{225}{2} \cdot 4$ .

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Step 3.2.1.1

Cancel the common factor of $2$ .

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Step 3.2.1.1.1

Move the leading negative in $- \frac{225}{2}$ into the numerator.

$75 x < \frac{- 225}{2} \cdot 4$

Step 3.2.1.1.2

Factor $2$ out of $4$ .

$75 x < \frac{- 225}{2} \cdot (2 (2))$

Step 3.2.1.1.3

Cancel the common factor.

$75 x < \frac{- 225}{2} \cdot (2 \cdot 2)$

Step 3.2.1.1.4

Rewrite the expression.

$75 x < - 225 \cdot 2$

Step 3.2.1.2

Multiply $- 225$ by $2$ .

$75 x < - 450$

Step 4

Divide each term in $75 x < - 450$ by $75$ and simplify.

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Step 4.1

Divide each term in $75 x < - 450$ by $75$ .

$\frac{75 x}{75} < \frac{- 450}{75}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $75$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{75 x}{75} < \frac{- 450}{75}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 450}{75}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 450$ by $75$ .

$x < - 6$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 6$

Interval Notation:

$(- \infty, - 6)$