Algebra Examples

$- \frac{1}{3} h \geq 8$

Step 1

Multiply each term in $- \frac{1}{3} h \geq 8$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{3} h \cdot - 3 \leq 8 \cdot - 3$

Step 2

Simplify the left side.

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Step 2.1

Combine $h$ and $\frac{1}{3}$ .

$- \frac{h}{3} \cdot - 3 \leq 8 \cdot - 3$

Step 2.2

Cancel the common factor of $3$ .

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Step 2.2.1

Move the leading negative in $- \frac{h}{3}$ into the numerator.

$\frac{- h}{3} \cdot - 3 \leq 8 \cdot - 3$

Step 2.2.2

Factor $3$ out of $- 3$ .

$\frac{- h}{3} \cdot (3 (- 1)) \leq 8 \cdot - 3$

Step 2.2.3

Cancel the common factor.

$\frac{- h}{3} \cdot (3 \cdot - 1) \leq 8 \cdot - 3$

Step 2.2.4

Rewrite the expression.

$- h \cdot - 1 \leq 8 \cdot - 3$

Step 2.3

Multiply.

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

$1 h \leq 8 \cdot - 3$

Step 2.3.2

Multiply $h$ by $1$ .

$h \leq 8 \cdot - 3$

Step 3

Simplify the right side.

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Step 3.1

Multiply $8$ by $- 3$ .

$h \leq - 24$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$h \leq - 24$

Interval Notation:

$(- \infty, - 24]$