Algebra Examples

$- \frac{1}{3} (p + 9) \leq 4$

Step 1

Multiply each term in $- \frac{1}{3} \cdot (p + 9) \leq 4$ by $- 3$ to eliminate the fractions.

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Step 1.1

Multiply each term in $- \frac{1}{3} \cdot (p + 9) \leq 4$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$- \frac{1}{3} \cdot (p + 9) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Apply the distributive property.

$(- \frac{1}{3} p - \frac{1}{3} \cdot 9) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.2

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

$(- \frac{p}{3} - \frac{1}{3} \cdot 9) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.3

Cancel the common factor of $3$ .

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Step 1.2.3.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$(- \frac{p}{3} + \frac{- 1}{3} \cdot 9) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.3.2

Factor $3$ out of $9$ .

$(- \frac{p}{3} + \frac{- 1}{3} \cdot (3 (3))) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.3.3

Cancel the common factor.

$(- \frac{p}{3} + \frac{- 1}{3} \cdot (3 \cdot 3)) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.3.4

Rewrite the expression.

$(- \frac{p}{3} - 1 \cdot 3) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.4

Multiply $- 1$ by $3$ .

$(- \frac{p}{3} - 3) \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.5

Apply the distributive property.

$- \frac{p}{3} \cdot - 3 - 3 \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.6

Cancel the common factor of $3$ .

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Step 1.2.6.1

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

$\frac{- p}{3} \cdot - 3 - 3 \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.6.2

Factor $3$ out of $- 3$ .

$\frac{- p}{3} \cdot (3 (- 1)) - 3 \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.6.3

Cancel the common factor.

$\frac{- p}{3} \cdot (3 \cdot - 1) - 3 \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.6.4

Rewrite the expression.

$- p \cdot - 1 - 3 \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.7

Multiply.

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Step 1.2.7.1

Multiply $- 1$ by $- 1$ .

$1 p - 3 \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.7.2

Multiply $p$ by $1$ .

$p - 3 \cdot - 3 \geq 4 \cdot - 3$

Step 1.2.7.3

Multiply $- 3$ by $- 3$ .

$p + 9 \geq 4 \cdot - 3$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $4$ by $- 3$ .

$p + 9 \geq - 12$

Step 2

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

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Step 2.1

Subtract $9$ from both sides of the inequality.

$p \geq - 12 - 9$

Step 2.2

Subtract $9$ from $- 12$ .

$p \geq - 21$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$p \geq - 21$

Interval Notation:

$[- 21, \infty)$