solve the compound inequality

3x-5>-17 and 4x+3<15
my answer: -4<x<3

Answered in another post.

To solve the compound inequality 3x - 5 > -17 and 4x + 3 < 15, you need to solve each inequality separately and then find the intersection of the solutions.

Starting with the first inequality, 3x - 5 > -17, you can solve it by adding 5 to both sides:
3x - 5 + 5 > -17 + 5
3x > -12

Next, divide both sides by 3 to isolate x:
(3x)/3 > (-12)/3
x > -4

Moving on to the second inequality, 4x + 3 < 15, subtract 3 from both sides:
4x + 3 - 3 < 15 - 3
4x < 12

Then, dividing both sides by 4 gives you:
(4x)/4 < (12)/4
x < 3

Now, you have two separate solutions: x > -4 and x < 3. To find the intersection of these solutions, you need to find the values of x that satisfy both inequalities simultaneously.

Since x must be greater than -4 and less than 3, the final solution is: -4 < x < 3.