Finite Math Examples

$- \frac{1}{6} a < - 2$

Step 1

Multiply each term in $- \frac{1}{6} a < - 2$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{6} a \cdot - 6 > - 2 \cdot - 6$

Step 2

Simplify the left side.

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Step 2.1

Combine $a$ and $\frac{1}{6}$ .

$- \frac{a}{6} \cdot - 6 > - 2 \cdot - 6$

Step 2.2

Cancel the common factor of $6$ .

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Step 2.2.1

Move the leading negative in $- \frac{a}{6}$ into the numerator.

$\frac{- a}{6} \cdot - 6 > - 2 \cdot - 6$

Step 2.2.2

Factor $6$ out of $- 6$ .

$\frac{- a}{6} \cdot (6 (- 1)) > - 2 \cdot - 6$

Step 2.2.3

Cancel the common factor.

$\frac{- a}{6} \cdot (6 \cdot - 1) > - 2 \cdot - 6$

Step 2.2.4

Rewrite the expression.

$- a \cdot - 1 > - 2 \cdot - 6$

Step 2.3

Multiply.

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$1 a > - 2 \cdot - 6$

Step 2.3.2

Multiply $a$ by $1$ .

$a > - 2 \cdot - 6$

Step 3

Simplify the right side.

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Step 3.1

Multiply $- 2$ by $- 6$ .

$a > 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a > 12$

Interval Notation:

$(12, \infty)$