Algebra Examples

$x (x + 12) > {(x - 4)}^{2}$

Step 1

Simplify $x (x + 12)$ .

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Step 1.1

Rewrite.

$0 + 0 + x (x + 12) > {(x - 4)}^{2}$

Step 1.2

Simplify by adding zeros.

$x (x + 12) > {(x - 4)}^{2}$

Step 1.3

Apply the distributive property.

$x \cdot x + x \cdot 12 > {(x - 4)}^{2}$

Step 1.4

Simplify the expression.

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Step 1.4.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 12 > {(x - 4)}^{2}$

Step 1.4.2

Move $12$ to the left of $x$ .

$x^{2} + 12 x > {(x - 4)}^{2}$

Step 2

Simplify ${(x - 4)}^{2}$ .

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Step 2.1

Rewrite ${(x - 4)}^{2}$ as $(x - 4) (x - 4)$ .

$x^{2} + 12 x > (x - 4) (x - 4)$

Step 2.2

Expand $(x - 4) (x - 4)$ using the FOIL Method.

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Step 2.2.1

Apply the distributive property.

$x^{2} + 12 x > x (x - 4) - 4 (x - 4)$

Step 2.2.2

Apply the distributive property.

$x^{2} + 12 x > x \cdot x + x \cdot - 4 - 4 (x - 4)$

Step 2.2.3

Apply the distributive property.

$x^{2} + 12 x > x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$x^{2} + 12 x > x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4$

Step 2.3.1.2

Move $- 4$ to the left of $x$ .

$x^{2} + 12 x > x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4$

Step 2.3.1.3

Multiply $- 4$ by $- 4$ .

$x^{2} + 12 x > x^{2} - 4 x - 4 x + 16$

Step 2.3.2

Subtract $4 x$ from $- 4 x$ .

$x^{2} + 12 x > x^{2} - 8 x + 16$

Step 3

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

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Step 3.1

Subtract $x^{2}$ from both sides of the inequality.

$x^{2} + 12 x - x^{2} > - 8 x + 16$

Step 3.2

Add $8 x$ to both sides of the inequality.

$x^{2} + 12 x - x^{2} + 8 x > 16$

Step 3.3

Combine the opposite terms in $x^{2} + 12 x - x^{2} + 8 x$ .

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Step 3.3.1

Subtract $x^{2}$ from $x^{2}$ .

$12 x + 0 + 8 x > 16$

Step 3.3.2

Add $12 x$ and $0$ .

$12 x + 8 x > 16$

Step 3.4

Add $12 x$ and $8 x$ .

$20 x > 16$

Step 4

Divide each term in $20 x > 16$ by $20$ and simplify.

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Step 4.1

Divide each term in $20 x > 16$ by $20$ .

$\frac{20 x}{20} > \frac{16}{20}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $20$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{20 x}{20} > \frac{16}{20}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x > \frac{16}{20}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $16$ and $20$ .

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Step 4.3.1.1

Factor $4$ out of $16$ .

$x > \frac{4 (4)}{20}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $4$ out of $20$ .

$x > \frac{4 \cdot 4}{4 \cdot 5}$

Step 4.3.1.2.2

Cancel the common factor.

$x > \frac{4 \cdot 4}{4 \cdot 5}$

Step 4.3.1.2.3

Rewrite the expression.

$x > \frac{4}{5}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{4}{5}$

Interval Notation:

$(\frac{4}{5}, \infty)$

Step 6