Algebra Examples

$a (a - 1) - (a^{2} + a) < 34$

Step 1

Simplify $a (a - 1) - (a^{2} + a)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$a \cdot a + a \cdot - 1 - (a^{2} + a) < 34$

Step 1.1.2

Multiply $a$ by $a$ .

$a^{2} + a \cdot - 1 - (a^{2} + a) < 34$

Step 1.1.3

Move $- 1$ to the left of $a$ .

$a^{2} - 1 \cdot a - (a^{2} + a) < 34$

Step 1.1.4

Rewrite $- 1 a$ as $- a$ .

$a^{2} - a - (a^{2} + a) < 34$

Step 1.1.5

Apply the distributive property.

$a^{2} - a - a^{2} - a < 34$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Combine the opposite terms in $a^{2} - a - a^{2} - a$ .

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Step 1.2.1.1

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

$- a + 0 - a < 34$

Step 1.2.1.2

Add $- a$ and $0$ .

$- a - a < 34$

Step 1.2.2

Subtract $a$ from $- a$ .

$- 2 a < 34$

Step 2

Divide each term in $- 2 a < 34$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 a < 34$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 a}{- 2} > \frac{34}{- 2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 a}{- 2} > \frac{34}{- 2}$

Step 2.2.1.2

Divide $a$ by $1$ .

$a > \frac{34}{- 2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $34$ by $- 2$ .

$a > - 17$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$a > - 17$

Interval Notation:

$(- 17, \infty)$

Step 4