Math

QuestionSolve for aa: 3a+2>3a633a + 2 > \frac{3a - 6}{3}, a>2a > -2, a<0a < 0, a>0a > 0, a<2a < -2.

Studdy Solution

STEP 1

Assumptions1. The given inequalities are 3a+>3a633a + > \frac{3a -6}{3} and a>a > -. . We need to find the range of values for aa that satisfy both inequalities.

STEP 2

First, let's simplify the first inequality. We can do this by multiplying both sides by to remove the fraction.
(a+2)>a6(a +2) >a -6

STEP 3

Now, distribute the3 on the left side of the inequality.
9a+6>3a69a +6 >3a -6

STEP 4

Next, let's isolate aa by subtracting 3a3a from both sides of the inequality.
9a3a+6>69a -3a +6 > -6

STEP 5

implify the left side of the inequality.
a+>a + > -

STEP 6

Then, subtract6 from both sides of the inequality to isolate aa.
6a>126a > -12

STEP 7

Finally, divide both sides of the inequality by6 to solve for aa.
a>2a > -2

STEP 8

Now, we have two inequalities a>2a > -2 and a>2a > -2. Both inequalities give the same range for aa, which is a>2a > -2.
Therefore, the solution to the system of inequalities is a>2a > -2.

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