Algebra Examples

$0.2 x^{2} - 0.2 (x - 6) (x + 6) > 3.6 x$

Step 1

Simplify $0.2 x^{2} - 0.2 (x - 6) (x + 6)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$0.2 x^{2} + (- 0.2 x - 0.2 \cdot - 6) (x + 6) > 3.6 x$

Step 1.1.2

Multiply $- 0.2$ by $- 6$ .

$0.2 x^{2} + (- 0.2 x + 1.2) (x + 6) > 3.6 x$

Step 1.1.3

Expand $(- 0.2 x + 1.2) (x + 6)$ using the FOIL Method.

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Step 1.1.3.1

Apply the distributive property.

$0.2 x^{2} - 0.2 x (x + 6) + 1.2 (x + 6) > 3.6 x$

Step 1.1.3.2

Apply the distributive property.

$0.2 x^{2} - 0.2 x \cdot x - 0.2 x \cdot 6 + 1.2 (x + 6) > 3.6 x$

Step 1.1.3.3

Apply the distributive property.

$0.2 x^{2} - 0.2 x \cdot x - 0.2 x \cdot 6 + 1.2 x + 1.2 \cdot 6 > 3.6 x$

Step 1.1.4

Simplify and combine like terms.

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Step 1.1.4.1

Simplify each term.

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Step 1.1.4.1.1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1.4.1.1.1

Move $x$ .

$0.2 x^{2} - 0.2 (x \cdot x) - 0.2 x \cdot 6 + 1.2 x + 1.2 \cdot 6 > 3.6 x$

Step 1.1.4.1.1.2

Multiply $x$ by $x$ .

$0.2 x^{2} - 0.2 x^{2} - 0.2 x \cdot 6 + 1.2 x + 1.2 \cdot 6 > 3.6 x$

Step 1.1.4.1.2

Multiply $6$ by $- 0.2$ .

$0.2 x^{2} - 0.2 x^{2} - 1.2 x + 1.2 x + 1.2 \cdot 6 > 3.6 x$

Step 1.1.4.1.3

Multiply $1.2$ by $6$ .

$0.2 x^{2} - 0.2 x^{2} - 1.2 x + 1.2 x + 7.2 > 3.6 x$

Step 1.1.4.2

Add $- 1.2 x$ and $1.2 x$ .

$0.2 x^{2} - 0.2 x^{2} + 0 x + 7.2 > 3.6 x$

Step 1.1.5

Multiply $0$ by $x$ .

$0.2 x^{2} - 0.2 x^{2} + 0 + 7.2 > 3.6 x$

Step 1.1.6

Add $- 0.2 x^{2}$ and $0$ .

$0.2 x^{2} - 0.2 x^{2} + 7.2 > 3.6 x$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $0.2 x^{2}$ from $0.2 x^{2}$ .

$0 x^{2} + 7.2 > 3.6 x$

Step 1.2.2

Simplify the expression.

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Step 1.2.2.1

Multiply $0$ by $x^{2}$ .

$0 + 7.2 > 3.6 x$

Step 1.2.2.2

Add $0$ and $7.2$ .

$7.2 > 3.6 x$

Step 2

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

$3.6 x < 7.2$

Step 3

Divide each term in $3.6 x < 7.2$ by $3.6$ and simplify.

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Step 3.1

Divide each term in $3.6 x < 7.2$ by $3.6$ .

$\frac{3.6 x}{3.6} < \frac{7.2}{3.6}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3.6$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3.6 x}{3.6} < \frac{7.2}{3.6}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x < \frac{7.2}{3.6}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $7.2$ by $3.6$ .

$x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 2$

Interval Notation:

$(- \infty, 2)$

Step 5