Precalculus Examples

$20 - 2 p > - 2 (p + 2) + 4 p$

Step 1

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

$- 2 (p + 2) + 4 p < 20 - 2 p$

Step 2

Simplify $- 2 (p + 2) + 4 p$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$- 2 p - 2 \cdot 2 + 4 p < 20 - 2 p$

Step 2.1.2

Multiply $- 2$ by $2$ .

$- 2 p - 4 + 4 p < 20 - 2 p$

Step 2.2

Add $- 2 p$ and $4 p$ .

$2 p - 4 < 20 - 2 p$

Step 3

Move all terms containing $p$ to the left side of the inequality.

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Step 3.1

Add $2 p$ to both sides of the inequality.

$2 p - 4 + 2 p < 20$

Step 3.2

Add $2 p$ and $2 p$ .

$4 p - 4 < 20$

Step 4

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

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Step 4.1

Add $4$ to both sides of the inequality.

$4 p < 20 + 4$

Step 4.2

Add $20$ and $4$ .

$4 p < 24$

Step 5

Divide each term in $4 p < 24$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 p < 24$ by $4$ .

$\frac{4 p}{4} < \frac{24}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 p}{4} < \frac{24}{4}$

Step 5.2.1.2

Divide $p$ by $1$ .

$p < \frac{24}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $24$ by $4$ .

$p < 6$

Step 6

Convert the inequality to interval notation.

$(- \infty, 6)$

Step 7