Algebra Examples

$- 9 + 2 a < 3 a$

Step 1

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

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Step 1.1

Subtract $3 a$ from both sides of the inequality.

$- 9 + 2 a - 3 a < 0$

Step 1.2

Subtract $3 a$ from $2 a$ .

$- 9 - a < 0$

Step 2

Add $9$ to both sides of the inequality.

$- a < 9$

Step 3

Divide each term in $- a < 9$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- a < 9$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- a}{- 1} > \frac{9}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{a}{1} > \frac{9}{- 1}$

Step 3.2.2

Divide $a$ by $1$ .

$a > \frac{9}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $9$ by $- 1$ .

$a > - 9$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$a > - 9$

Interval Notation:

$(- 9, \infty)$