solve the compound inequality
3x-5>-17 and 4x+3<15
my answer: -4<x<3
Let's look at your problem:
3x - 5 > -17 and 4x + 3 < 15
x > -4 and x < 3
Or written another way: -4 < x < 3
Good job!
solve 4x-5>-13 or 3x-3>3
To solve the compound inequality 3x - 5 > -17 and 4x + 3 < 15, we need to solve each inequality separately and then find the intersection between the two solutions.
For the first inequality, 3x - 5 > -17, we can add 5 to both sides:
3x - 5 + 5 > -17 + 5
3x > -12
Now, we can divide both sides by 3 to isolate x:
3x/3 > -12/3
x > -4
For the second inequality, 4x + 3 < 15, we can subtract 3 from both sides:
4x + 3 - 3 < 15 - 3
4x < 12
Now, we can divide both sides by 4 to isolate x:
4x/4 < 12/4
x < 3
To find the intersection of the solutions, we look for the values of x that satisfy both inequalities. In this case, it is the values that are greater than -4 and less than 3. Therefore, the solution to the compound inequality is -4 < x < 3.
To solve this compound inequality, you will need to solve each inequality separately and then find the intersection of their solutions.
First, let's solve the first inequality:
3x - 5 > -17
Add 5 to both sides:
3x - 5 + 5 > -17 + 5
3x > -12
Divide both sides by 3 (since we want to isolate x):
3x/3 > -12/3
x > -4
Next, let's solve the second inequality:
4x + 3 < 15
Subtract 3 from both sides:
4x + 3 - 3 < 15 - 3
4x < 12
Divide both sides by 4:
4x/4 < 12/4
x < 3
Now, we need to find the intersection of these two solutions. Since both inequalities involve x being greater than or less than a certain value, the only numbers that satisfy both conditions are the ones between -4 and 3.
So, the solution to the compound inequality is: -4 < x < 3.