Algebra Examples

$x (x + 1) + 2 < x (x - 3) + 14$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$x \cdot x + x \cdot 1 + 2 < x (x - 3) + 14$

Step 1.2

Multiply $x$ by $x$ .

$x^{2} + x \cdot 1 + 2 < x (x - 3) + 14$

Step 1.3

Multiply $x$ by $1$ .

$x^{2} + x + 2 < x (x - 3) + 14$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$x^{2} + x + 2 < x \cdot x + x \cdot - 3 + 14$

Step 2.2

Multiply $x$ by $x$ .

$x^{2} + x + 2 < x^{2} + x \cdot - 3 + 14$

Step 2.3

Move $- 3$ to the left of $x$ .

$x^{2} + x + 2 < x^{2} - 3 x + 14$

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.

$x^{2} + x + 2 - x^{2} < - 3 x + 14$

Step 3.2

Add $3 x$ to both sides of the inequality.

$x^{2} + x + 2 - x^{2} + 3 x < 14$

Step 3.3

Combine the opposite terms in $x^{2} + x + 2 - x^{2} + 3 x$ .

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Step 3.3.1

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

$x + 2 + 0 + 3 x < 14$

Step 3.3.2

Add $x + 2$ and $0$ .

$x + 2 + 3 x < 14$

Step 3.4

Add $x$ and $3 x$ .

$4 x + 2 < 14$

Step 4

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

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Step 4.1

Subtract $2$ from both sides of the inequality.

$4 x < 14 - 2$

Step 4.2

Subtract $2$ from $14$ .

$4 x < 12$

Step 5

Divide each term in $4 x < 12$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 x < 12$ by $4$ .

$\frac{4 x}{4} < \frac{12}{4}$

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.

$\frac{4 x}{4} < \frac{12}{4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x < \frac{12}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $12$ by $4$ .

$x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 3$

Interval Notation:

$(- \infty, 3)$

Step 7