1. ## Inequality Application

The sum of a number and the original number increased by 5 is at least 12, what could be the original number?

MY WORK:

x + x + 5 > or = to 12

2x + 5 > or = to 12

2x > or = to 12 - 7

2x > or = to 7

x > or = to 7/2

But the answer is 4. How can this be?

2. Originally Posted by magentarita
The sum of a number and the original number increased by 5 is at least 12, what could be the original number?

MY WORK:

x + x + 5 > or = to 12

2x + 5 > or = to 12

2x > or = to 12 - 7

2x > or = to 7

x > or = to 7/2

But the answer is 4. How can this be?
Is there any sort of limit on the numbers that they must be integers?

7/2 is not an integer, but the nearest integer to 7/2 that satisfies the conditions is 4.

The question may be using the word 'number' in the same sense that 'number' theory is the theory of integers.

3. Originally Posted by magentarita
x > or = to 7/2

But the answer is 4. How can this be?
The solution to the inequality, in the real numbers, is all x > 7/2. In other words, the solution is an infinite set of values.

For "the answer" to be one number, either there are other restrictions on the value of x, or else there is some finite list of answer options from which you are supposed to choose. Or else "the answer" is wrong.

4. ## yes 4

Originally Posted by Mush
Is there any sort of limit on the numbers that they must be integers?

7/2 is not an integer, but the nearest integer to 7/2 that satisfies the conditions is 4.

The question may be using the word 'number' in the same sense that 'number' theory is the theory of integers.
Yes, the answer is 4 but no restrictions were given.