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

Answer 1

To solve the inequality 4x - 3 > 9, we first add 3 to both sides to isolate the variable:

4x - 3 + 3 > 9 + 3

This simplifies to:

4x > 12

Next, we divide both sides of the inequality by 4:

(4x)/4 > 12/4

This simplifies to:

x > 3

Now, let's solve the inequality x + 6 > -2. We begin by subtracting 6 from both sides to isolate the variable:

x + 6 - 6 > -2 - 6

This simplifies to:

x > -8

So, we have found that x is greater than 3 and x is greater than -8. To find the solution set, we take the intersection of these two inequalities:

x > 3 and x > -8

Since x must satisfy both of these conditions, we conclude that the solution set is:

x > 3