Solve the Inequality for a 3a+2>(3a-6)/3

$3 a + 2 > \frac{3 a - 6}{3}$

Step 1

Cancel the common factor of $3 a - 6$ and $3$ .

Factor $3$ out of $3 a$ .

$3 a + 2 > \frac{3 (a) - 6}{3}$

Factor $3$ out of $- 6$ .

$3 a + 2 > \frac{3 (a) + 3 \cdot - 2}{3}$

Factor $3$ out of $3 (a) + 3 (- 2)$ .

$3 a + 2 > \frac{3 (a - 2)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$3 a + 2 > \frac{3 (a - 2)}{3 (1)}$

Cancel the common factor.

$3 a + 2 > \frac{3 (a - 2)}{3 \cdot 1}$

Rewrite the expression.

$3 a + 2 > \frac{a - 2}{1}$

Divide $a - 2$ by $1$ .

$3 a + 2 > a - 2$

Step 2

Solve for $a$ .

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

Subtract $a$ from both sides of the inequality.

$3 a + 2 - a > - 2$

Subtract $a$ from $3 a$ .

$2 a + 2 > - 2$

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

Subtract $2$ from both sides of the inequality.

$2 a > - 2 - 2$

Subtract $2$ from $- 2$ .

$2 a > - 4$

Divide each term in $2 a > - 4$ by $2$ and simplify.

Divide each term in $2 a > - 4$ by $2$ .

$\frac{2 a}{2} > \frac{- 4}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 a}{2} > \frac{- 4}{2}$

Divide $a$ by $1$ .

$a > \frac{- 4}{2}$

Simplify the right side.

Divide $- 4$ by $2$ .

$a > - 2$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$a > - 2$

Interval Notation:

$(- 2, \infty)$

Solve the Inequality for a 3a+2>(3a-6)/3

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