Find the solution set of 4x−3>9 and x+6>−2 .
{3,−8} left brace 3 comma negative 8 right brace The solution set is null. The solution set is null. {x|x>3} left brace x vertical bar x greater than 3 right brace {x|x>−8}
The correct solution set is {x|x>-8}.
To find the solution set of 4x - 3 > 9, we can follow these steps:
Step 1: Add 3 to both sides of the inequality:
4x - 3 + 3 > 9 + 3
4x > 12
Step 2: Divide both sides of the inequality by 4:
(4x) / 4 > 12 / 4
x > 3
So, the solution to the inequality 4x - 3 > 9 is x > 3.
Next, let's find the solution set for x + 6 > -2:
Step 1: Subtract 6 from both sides of the inequality:
x + 6 - 6 > -2 - 6
x > -8
So, the solution to the inequality x + 6 > -2 is x > -8.
Combining the two solution sets together, we can say that the solution set for both inequalities is {x | x > 3} ∩ {x | x > -8}. In other words, the solution set is {x | x > 3}.
To find the solution set of the given inequalities, we need to solve each inequality separately and then find the overlapping region.
1. Solve the inequality 4x - 3 > 9:
Add 3 to both sides: 4x > 12
Divide both sides by 4 (since 4 is positive): x > 3
2. Solve the inequality x + 6 > -2:
Subtract 6 from both sides: x > -8
The overlapping region of the solutions is where both inequalities are satisfied. In this case, the overlapping region is x > 3 and x > -8.
Since both inequalities include x being greater than a specific value, the solution set can be expressed as {x | x > 3} and {x | x > -8}.
However, when we consider both inequalities together, we find that the solution set contains only values greater than 3 because 3 is a larger value than -8.
Therefore, the solution set is {x | x > 3}.