Finite Math Examples

$- 5 x - 7 > 27$

Step 1

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

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Step 1.1

Add $7$ to both sides of the inequality.

$- 5 x > 27 + 7$

Step 1.2

Add $27$ and $7$ .

$- 5 x > 34$

Step 2

Divide each term in $- 5 x > 34$ by $- 5$ and simplify.

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Step 2.1

Divide each term in $- 5 x > 34$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} < \frac{34}{- 5}$

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.

$\frac{- 5 x}{- 5} < \frac{34}{- 5}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x < \frac{34}{- 5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$x < - \frac{34}{5}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{34}{5}$

Interval Notation:

$(- \infty, - \frac{34}{5})$