Find the solution set of 4x−3>9 and x+6>−2.

Answer 1

To find the solution set, we will solve each inequality separately and then determine the intersection of the solution sets.

For the first inequality, 4x - 3 > 9, we can add 3 to both sides to isolate the x term:
4x - 3 + 3 > 9 + 3
4x > 12
Next, we divide both sides by 4 to solve for x:
(4x)/4 > 12/4
x > 3

For the second inequality, x + 6 > -2, we can subtract 6 from both sides to isolate the x term:
x + 6 - 6 > -2 - 6
x > -8

Now, we can look at the intersection of the solution sets of both inequalities, which is the set of values that satisfy both inequalities. In this case, we can see that x must be greater than 3 and greater than -8. Therefore, the solution set is x > 3.