Finite Math Examples

$\frac{2 k - 5}{- 4} > 5$

Step 1

Multiply both sides by $- 4$ .

$\frac{2 k - 5}{- 4} \cdot - 4 < 5 \cdot - 4$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{2 k - 5}{- 4} \cdot - 4$ .

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Step 2.1.1.1

Cancel the common factor of $4$ .

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Step 2.1.1.1.1

Factor $4$ out of $- 4$ .

$\frac{2 k - 5}{4 (- 1)} \cdot - 4 < 5 \cdot - 4$

Step 2.1.1.1.2

Factor $4$ out of $- 4$ .

$\frac{2 k - 5}{4 \cdot - 1} \cdot (4 \cdot - 1) < 5 \cdot - 4$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{2 k - 5}{4 \cdot - 1} \cdot (4 \cdot - 1) < 5 \cdot - 4$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{2 k - 5}{- 1} \cdot - 1 < 5 \cdot - 4$

Step 2.1.1.2

Combine $\frac{2 k - 5}{- 1}$ and $- 1$ .

$\frac{(2 k - 5) \cdot - 1}{- 1} < 5 \cdot - 4$

Step 2.1.1.3

Simplify the expression.

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Step 2.1.1.3.1

Move the negative one from the denominator of $\frac{(2 k - 5) \cdot - 1}{- 1}$ .

$- 1 \cdot ((2 k - 5) \cdot - 1) < 5 \cdot - 4$

Step 2.1.1.3.2

Rewrite $- 1 \cdot ((2 k - 5) \cdot - 1)$ as $- ((2 k - 5) \cdot - 1)$ .

$- ((2 k - 5) \cdot - 1) < 5 \cdot - 4$

Step 2.1.1.4

Apply the distributive property.

$- (2 k \cdot - 1 - 5 \cdot - 1) < 5 \cdot - 4$

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $- 1$ by $2$ .

$- (- 2 k - 5 \cdot - 1) < 5 \cdot - 4$

Step 2.1.1.5.2

Multiply $- 5$ by $- 1$ .

$- (- 2 k + 5) < 5 \cdot - 4$

Step 2.1.1.6

Apply the distributive property.

$- (- 2 k) - 1 \cdot 5 < 5 \cdot - 4$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 2$ by $- 1$ .

$2 k - 1 \cdot 5 < 5 \cdot - 4$

Step 2.1.1.7.2

Multiply $- 1$ by $5$ .

$2 k - 5 < 5 \cdot - 4$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $5$ by $- 4$ .

$2 k - 5 < - 20$

Step 3

Solve for $k$ .

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Step 3.1

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

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Step 3.1.1

Add $5$ to both sides of the inequality.

$2 k < - 20 + 5$

Step 3.1.2

Add $- 20$ and $5$ .

$2 k < - 15$

Step 3.2

Divide each term in $2 k < - 15$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 k < - 15$ by $2$ .

$\frac{2 k}{2} < \frac{- 15}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 k}{2} < \frac{- 15}{2}$

Step 3.2.2.1.2

Divide $k$ by $1$ .

$k < \frac{- 15}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Move the negative in front of the fraction.

$k < - \frac{15}{2}$

Step 4

Convert the inequality to interval notation.

$(- \infty, - \frac{15}{2})$

Step 5