Find the solution set of 4x−3>9 and x+6>−2
To solve the inequality 4x - 3 > 9, add 3 to both sides of the inequality to isolate the variable:
4x - 3 + 3 > 9 + 3
4x > 12
Next, divide both sides of the inequality by 4 to solve for x:
(4x)/4 > 12/4
x > 3
So the first inequality is satisfied when x is greater than 3.
Moving on to the second inequality, x + 6 > -2, subtract 6 from both sides of the inequality:
x + 6 - 6 > -2 - 6
x > -8
So the second inequality is satisfied when x is greater than -8.
Combining the solution sets of both inequalities, the solution set for the system of inequalities 4x - 3 > 9 and x + 6 > -2 is x > 3 and x > -8. However, since the second inequality is always true for any x, we can simplify the solution set to x > 3.