Algebra Examples

$\frac{c + 9}{- 5} < - 2$

Step 1

Multiply both sides by $- 5$ .

$\frac{c + 9}{- 5} \cdot - 5 > - 2 \cdot - 5$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{c + 9}{- 5} \cdot - 5$ .

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Cancel the common factor of $5$ .

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Step 2.1.1.1.1.1

Factor $5$ out of $- 5$ .

$\frac{c + 9}{5 (- 1)} \cdot - 5 > - 2 \cdot - 5$

Step 2.1.1.1.1.2

Factor $5$ out of $- 5$ .

$\frac{c + 9}{5 \cdot - 1} \cdot (5 \cdot - 1) > - 2 \cdot - 5$

Step 2.1.1.1.1.3

Cancel the common factor.

$\frac{c + 9}{5 \cdot - 1} \cdot (5 \cdot - 1) > - 2 \cdot - 5$

Step 2.1.1.1.1.4

Rewrite the expression.

$\frac{c + 9}{- 1} \cdot - 1 > - 2 \cdot - 5$

Step 2.1.1.1.2

Combine $\frac{c + 9}{- 1}$ and $- 1$ .

$\frac{(c + 9) \cdot - 1}{- 1} > - 2 \cdot - 5$

Step 2.1.1.1.3

Simplify the expression.

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Step 2.1.1.1.3.1

Move the negative one from the denominator of $\frac{(c + 9) \cdot - 1}{- 1}$ .

$- 1 \cdot ((c + 9) \cdot - 1) > - 2 \cdot - 5$

Step 2.1.1.1.3.2

Rewrite $- 1 \cdot ((c + 9) \cdot - 1)$ as $- ((c + 9) \cdot - 1)$ .

$- ((c + 9) \cdot - 1) > - 2 \cdot - 5$

Step 2.1.1.1.4

Apply the distributive property.

$- (c \cdot - 1 + 9 \cdot - 1) > - 2 \cdot - 5$

Step 2.1.1.1.5

Simplify the expression.

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Step 2.1.1.1.5.1

Move $- 1$ to the left of $c$ .

$- (- 1 \cdot c + 9 \cdot - 1) > - 2 \cdot - 5$

Step 2.1.1.1.5.2

Multiply $9$ by $- 1$ .

$- (- 1 \cdot c - 9) > - 2 \cdot - 5$

Step 2.1.1.2

Rewrite $- 1 c$ as $- c$ .

$- (- c - 9) > - 2 \cdot - 5$

Step 2.1.1.3

Apply the distributive property.

$- - c - - 9 > - 2 \cdot - 5$

Step 2.1.1.4

Multiply $- - c$ .

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

$1 c - - 9 > - 2 \cdot - 5$

Step 2.1.1.4.2

Multiply $c$ by $1$ .

$c - - 9 > - 2 \cdot - 5$

Step 2.1.1.5

Multiply $- 1$ by $- 9$ .

$c + 9 > - 2 \cdot - 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 2$ by $- 5$ .

$c + 9 > 10$

Step 3

Move all terms not containing $c$ to the right side of the inequality.

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Step 3.1

Subtract $9$ from both sides of the inequality.

$c > 10 - 9$

Step 3.2

Subtract $9$ from $10$ .

$c > 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$c > 1$

Interval Notation:

$(1, \infty)$