Find the solution set of 4x−3>9 and x+6>−2 . Responses {x|x>−8} left brace x vertical bar x greater than negative 8 right brace {3,−8} left brace 3 comma negative 8 right brace The solution set is null. The solution set is null. {x|x>3}
The correct solution is {x|x>3}.
To find the solution set of the inequalities 4x - 3 > 9 and x + 6 > -2, we will solve them step by step.
For the first inequality:
4x - 3 > 9
We will start by adding 3 to both sides:
4x - 3 + 3 > 9 + 3
4x > 12
Next, we divide both sides by 4 to isolate x:
4x/4 > 12/4
x > 3
So, the first inequality simplifies to x > 3.
Now, let's move on to the second inequality:
x + 6 > -2
We will subtract 6 from both sides:
x + 6 - 6 > -2 - 6
x > -8
So, the second inequality simplifies to x > -8.
Now, let's combine the solution sets of both inequalities:
{x | x > 3} and {x | x > -8}
The intersection of these solution sets is:
{x | x > 3} ∩ {x | x > -8}
Since both inequalities have x > 3 as a common condition, the solution set is:
{x | x > 3}
Therefore, the solution set for the given system of inequalities is {x | x > 3}.
To find the solution set for the given inequalities, we need to solve each inequality separately and then determine their intersection.
Let's start with the first inequality: 4x - 3 > 9.
1. Add 3 to both sides: 4x > 12.
2. Divide both sides by 4: x > 3.
So, the solution to the first inequality is x > 3.
Now, let's move on to the second inequality: x + 6 > -2.
1. Subtract 6 from both sides: x > -8.
So, the solution to the second inequality is x > -8.
To find the intersection of the solution sets, we need to find the values that satisfy both inequalities.
The only values that satisfy both inequalities are those that are greater than both 3 and -8. Therefore, the solution set is {x | x > 3 and x > -8}.
Since any value greater than 3 is also greater than -8, we can simplify the solution set as {x | x > -8}.
Therefore, the solution set for the given inequalities is {x | x > -8}.