Algebra Examples

$- 9 < - \frac{1}{5} x$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$- \frac{1}{5} x > - 9$

Step 2

Multiply each term in $- \frac{1}{5} x > - 9$ by $- 5$ to eliminate the fractions.

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Step 2.1

Multiply each term in $- \frac{1}{5} x > - 9$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{5} x \cdot - 5 < - 9 \cdot - 5$

Step 2.2

Simplify the left side.

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Step 2.2.1

Combine $x$ and $\frac{1}{5}$ .

$- \frac{x}{5} \cdot - 5 < - 9 \cdot - 5$

Step 2.2.2

Cancel the common factor of $5$ .

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Step 2.2.2.1

Move the leading negative in $- \frac{x}{5}$ into the numerator.

$\frac{- x}{5} \cdot - 5 < - 9 \cdot - 5$

Step 2.2.2.2

Factor $5$ out of $- 5$ .

$\frac{- x}{5} \cdot (5 (- 1)) < - 9 \cdot - 5$

Step 2.2.2.3

Cancel the common factor.

$\frac{- x}{5} \cdot (5 \cdot - 1) < - 9 \cdot - 5$

Step 2.2.2.4

Rewrite the expression.

$- x \cdot - 1 < - 9 \cdot - 5$

Step 2.2.3

Multiply.

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Step 2.2.3.1

Multiply $- 1$ by $- 1$ .

$1 x < - 9 \cdot - 5$

Step 2.2.3.2

Multiply $x$ by $1$ .

$x < - 9 \cdot - 5$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $- 9$ by $- 5$ .

$x < 45$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < 45$

Interval Notation:

$(- \infty, 45)$