Finite Math Examples

$\frac{5 x - 4}{- 7} > 4$

Step 1

Multiply both sides by $- 7$ .

$\frac{5 x - 4}{- 7} \cdot - 7 < 4 \cdot - 7$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5 x - 4}{- 7} \cdot - 7$ .

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Step 2.1.1.1

Cancel the common factor of $7$ .

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Step 2.1.1.1.1

Factor $7$ out of $- 7$ .

$\frac{5 x - 4}{7 (- 1)} \cdot - 7 < 4 \cdot - 7$

Step 2.1.1.1.2

Factor $7$ out of $- 7$ .

$\frac{5 x - 4}{7 \cdot - 1} \cdot (7 \cdot - 1) < 4 \cdot - 7$

Step 2.1.1.1.3

Cancel the common factor.

$\frac{5 x - 4}{7 \cdot - 1} \cdot (7 \cdot - 1) < 4 \cdot - 7$

Step 2.1.1.1.4

Rewrite the expression.

$\frac{5 x - 4}{- 1} \cdot - 1 < 4 \cdot - 7$

Step 2.1.1.2

Combine $\frac{5 x - 4}{- 1}$ and $- 1$ .

$\frac{(5 x - 4) \cdot - 1}{- 1} < 4 \cdot - 7$

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 $\frac{(5 x - 4) \cdot - 1}{- 1}$ .

$- 1 \cdot ((5 x - 4) \cdot - 1) < 4 \cdot - 7$

Step 2.1.1.3.2

Rewrite $- 1 \cdot ((5 x - 4) \cdot - 1)$ as $- ((5 x - 4) \cdot - 1)$ .

$- ((5 x - 4) \cdot - 1) < 4 \cdot - 7$

Step 2.1.1.4

Apply the distributive property.

$- (5 x \cdot - 1 - 4 \cdot - 1) < 4 \cdot - 7$

Step 2.1.1.5

Multiply.

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Step 2.1.1.5.1

Multiply $- 1$ by $5$ .

$- (- 5 x - 4 \cdot - 1) < 4 \cdot - 7$

Step 2.1.1.5.2

Multiply $- 4$ by $- 1$ .

$- (- 5 x + 4) < 4 \cdot - 7$

Step 2.1.1.6

Apply the distributive property.

$- (- 5 x) - 1 \cdot 4 < 4 \cdot - 7$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 5$ by $- 1$ .

$5 x - 1 \cdot 4 < 4 \cdot - 7$

Step 2.1.1.7.2

Multiply $- 1$ by $4$ .

$5 x - 4 < 4 \cdot - 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $4$ by $- 7$ .

$5 x - 4 < - 28$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Add $4$ to both sides of the inequality.

$5 x < - 28 + 4$

Step 3.1.2

Add $- 28$ and $4$ .

$5 x < - 24$

Step 3.2

Divide each term in $5 x < - 24$ by $5$ and simplify.

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Step 3.2.1

Divide each term in $5 x < - 24$ by $5$ .

$\frac{5 x}{5} < \frac{- 24}{5}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} < \frac{- 24}{5}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 24}{5}$

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.

$x < - \frac{24}{5}$

Step 4

Convert the inequality to interval notation.

$(- \infty, - \frac{24}{5})$

Step 5