Find the solution set of 4x−3>9 and x+6>−2.
To find the solution set, we will solve each inequality separately and then determine the intersection of the solution sets.
For the first inequality, 4x - 3 > 9, we can add 3 to both sides to isolate the x term:
4x - 3 + 3 > 9 + 3
4x > 12
Next, we divide both sides by 4 to solve for x:
(4x)/4 > 12/4
x > 3
For the second inequality, x + 6 > -2, we can subtract 6 from both sides to isolate the x term:
x + 6 - 6 > -2 - 6
x > -8
Now, we can look at the intersection of the solution sets of both inequalities, which is the set of values that satisfy both inequalities. In this case, we can see that x must be greater than 3 and greater than -8. Therefore, the solution set is x > 3.
To find the solution set of the given inequalities, we need to solve each inequality separately. Let's start with the first inequality:
4x - 3 > 9
To solve this inequality, we will isolate the variable x.
Adding 3 to both sides of the inequality:
4x - 3 + 3 > 9 + 3
4x > 12
Dividing both sides of the inequality by 4 (since the coefficient of x is 4 and we want x to be alone):
(4x)/4 > 12/4
x > 3
Therefore, the solution to the first inequality is x > 3.
Now, let's move on to the second inequality:
x + 6 > -2
To solve this inequality, we will isolate the variable x.
Subtracting 6 from both sides of the inequality:
x + 6 - 6 > -2 - 6
x > -8
Therefore, the solution to the second inequality is x > -8.
To find the solution set of both inequalities combined, we take the intersection of the individual solution sets.
Since both inequalities have the condition that x is greater than a certain value, the solution set is the set of all x greater than the greater value in the two solutions.
In this case, the greater value is 3 (from the first inequality). Therefore, the solution set for both inequalities combined is x > 3.
To solve these inequalities, we'll need to solve each one separately and then find the intersection of the solution sets.
Let's start with the first inequality: 4x-3 > 9
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 set for the first inequality is x > 3.
Now let's move on to the second inequality: x + 6 > -2
Step 1: Subtract 6 from both sides of the inequality:
(x + 6) - 6 > -2 - 6
x > -8
So the solution set for the second inequality is x > -8.
To find the intersection of the solution sets, we need to find the values that satisfy both inequalities. Since both inequalities have x > values, we can see that the solution set is x > 3.
Therefore, the solution set for the given system of inequalities is x > 3.