Pre-Algebra Examples

$- \frac{2}{3} n \leq 16$

Step 1

Multiply each term in $- \frac{2}{3} n \leq 16$ by $- \frac{3}{2}$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{2}{3} n (- \frac{3}{2}) \geq 16 (- \frac{3}{2})$

Step 2

Simplify the left side.

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Step 2.1

Combine $n$ and $\frac{2}{3}$ .

$- \frac{n \cdot 2}{3} (- \frac{3}{2}) \geq 16 (- \frac{3}{2})$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Move the leading negative in $- \frac{n \cdot 2}{3}$ into the numerator.

$\frac{- n \cdot 2}{3} (- \frac{3}{2}) \geq 16 (- \frac{3}{2})$

Step 2.2.2

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$\frac{- n \cdot 2}{3} \cdot \frac{- 3}{2} \geq 16 (- \frac{3}{2})$

Step 2.2.3

Factor $2$ out of $- n \cdot 2$ .

$\frac{2 \cdot (- n)}{3} \cdot \frac{- 3}{2} \geq 16 (- \frac{3}{2})$

Step 2.2.4

Cancel the common factor.

$\frac{2 \cdot (- n)}{3} \cdot \frac{- 3}{2} \geq 16 (- \frac{3}{2})$

Step 2.2.5

Rewrite the expression.

$\frac{- n}{3} \cdot - 3 \geq 16 (- \frac{3}{2})$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Factor $3$ out of $- 3$ .

$\frac{- n}{3} \cdot (3 (- 1)) \geq 16 (- \frac{3}{2})$

Step 2.3.2

Cancel the common factor.

$\frac{- n}{3} \cdot (3 \cdot - 1) \geq 16 (- \frac{3}{2})$

Step 2.3.3

Rewrite the expression.

$- n \cdot - 1 \geq 16 (- \frac{3}{2})$

Step 2.4

Multiply.

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Step 2.4.1

Multiply $- 1$ by $- 1$ .

$1 n \geq 16 (- \frac{3}{2})$

Step 2.4.2

Multiply $n$ by $1$ .

$n \geq 16 (- \frac{3}{2})$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$n \geq 16 (\frac{- 3}{2})$

Step 3.1.2

Factor $2$ out of $16$ .

$n \geq 2 (8) \frac{- 3}{2}$

Step 3.1.3

Cancel the common factor.

$n \geq 2 \cdot 8 \frac{- 3}{2}$

Step 3.1.4

Rewrite the expression.

$n \geq 8 \cdot - 3$

Step 3.2

Multiply $8$ by $- 3$ .

$n \geq - 24$

Step 4