Pre-Algebra Examples

$75 < - 5 (4 x + 1)$

Step 1

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

$- 5 (4 x + 1) > 75$

Step 2

Divide each term in $- 5 (4 x + 1) > 75$ by $- 5$ and simplify.

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Step 2.1

Divide each term in $- 5 (4 x + 1) > 75$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 (4 x + 1)}{- 5} < \frac{75}{- 5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 5 (4 x + 1)}{- 5} < \frac{75}{- 5}$

Step 2.2.1.2

Divide $4 x + 1$ by $1$ .

$4 x + 1 < \frac{75}{- 5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $75$ by $- 5$ .

$4 x + 1 < - 15$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the inequality.

$4 x < - 15 - 1$

Step 3.2

Subtract $1$ from $- 15$ .

$4 x < - 16$

Step 4

Divide each term in $4 x < - 16$ by $4$ and simplify.

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Step 4.1

Divide each term in $4 x < - 16$ by $4$ .

$\frac{4 x}{4} < \frac{- 16}{4}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} < \frac{- 16}{4}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x < \frac{- 16}{4}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 16$ by $4$ .

$x < - 4$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < - 4$

Interval Notation:

$(- \infty, - 4)$