Finite Math Examples

$- 8 < \frac{1}{2} x - 6$

Step 1

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

$\frac{1}{2} x - 6 > - 8$

Step 2

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - 6 > - 8$

Step 3

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

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Step 3.1

Add $6$ to both sides of the inequality.

$\frac{x}{2} > - 8 + 6$

Step 3.2

Add $- 8$ and $6$ .

$\frac{x}{2} > - 2$

Step 4

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 > - 2 \cdot 2$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $2$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{x}{2} \cdot 2 > - 2 \cdot 2$

Step 5.1.1.2

Rewrite the expression.

$x > - 2 \cdot 2$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 2$ by $2$ .

$x > - 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > - 4$

Interval Notation:

$(- 4, \infty)$