Algebra Examples

$\frac{r}{5} > - 3$ OR $4 r < - 100$

Step 1

Solve $\frac{r}{5} > - 3$ for $r$ .

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Step 1.1

Multiply both sides by $5$ .

$\frac{r}{5} \cdot 5 > - 3 \cdot 5$

Step 1.2

Simplify.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Cancel the common factor of $5$ .

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Step 1.2.1.1.1

Cancel the common factor.

$\frac{r}{5} \cdot 5 > - 3 \cdot 5$

Step 1.2.1.1.2

Rewrite the expression.

$r > - 3 \cdot 5$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Multiply $- 3$ by $5$ .

$r > - 15$

Step 2

Divide each term in $4 r < - 100$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 r < - 100$ by $4$ .

$\frac{4 r}{4} < \frac{- 100}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 r}{4} < \frac{- 100}{4}$

Step 2.2.1.2

Divide $r$ by $1$ .

$r < \frac{- 100}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 100$ by $4$ .

$r < - 25$

Step 3

Find the intersection of $r > - 15$ and $r < - 25$ .

No solution