A couple compound Inequality Questions?

Question

3x - 4 > 1 OR 2x + 1 < 15..The solution for this is said to be All Real numbers? Why is this so? I came up with x>-1 or x < 7

5x/2 + 1 >=3 AND x - 2/3 >=4/3 The solution for this is said to be x>=2. I came up with x>=0.8 and x >=2

S H MC...Can you email or Im me?

Answer 1

You came up with x > -1 OR x < 7. The "or" is key. It can be less than 7, or greater than -1. There's no real number that doesn't fit the solution.

For the second one, you came up with x >= 0.8 AND x >= 2. Similarly, the "and" is the key here. Anything greater than or equal to 2 is going to be greater than 0.8, fulfilling both conditions. The same cannot be said if the numbers are reversed.

To sum it up, if the problem has an "or" condition, every solution must solve at least one inequality. If the condition is "and", every solution must solve ALL inequalities.

Answer 2

3x-4>1 so 3x>5 so x >5/3
2x+1<15 2x so 2x<14 so x <7
So x is any number >5 /3 and any number < 7.
Sincce x is any number < 7 this covers all numbers from negative infinity to almost 7. But x>5/3. Therefore x is annnumber from just over 5/3 to positive infinity. This ,then, covers all the real numbers. It is the OR function that makes this so.


5x/2+1>=3 so 5x/2>=2 so 5x>=4 so x>=0.8
x-2/3 >=4/3 so x>= 2

This is an AND function which means that both functions must be true. But if X>=2, it can not also be >=4/3. Therefore, only x>2 satisfies this AND function.

Answer 3

With an OR compound inequality, so long as it works for one inequality it is a solution. Graph your solution on a number line. You will see that you shade the entire number line, i.e. EVERY number is either greater than -1 or less than 7.

With the AND, a solution must work in BOTH inequalities. If a number is greater than or equal to 2, then it MUST also be greater than or equal to 0.8. Again you can see this when you graph. (In an AND the solution set is the overlap of the graphs!)

Answer 4

"I came up with x>-1 or x < 7 "... Figure out which numbers meet these conditions and you'll know why the answer is all real numbers.

"I came up with x>=0.8 and x >=2"... If x has to be at least 2, then does x>=0.8 matter?

Answer 5

the 2nd one would be x>2 because the question says AND and since if you said it could be greater than .8 or 2, x could end up being something like 1 which is not greater than .8 AND 2

Answer 6

The second one is so because the signs are the same way (>) so u choose the greater one(2). The first one i dunno srry.