A certain number is halved, then increased by 3. The result lies between 5 and 7.
Between which two values does the number lie? Write an inequeality for this?
7>(.5n+3)>5
4
Let's call the unknown number "x".
According to the given information, the number is halved, then increased by 3. Mathematically, this can be represented as (x/2) + 3.
The result of this operation lies between 5 and 7. So, we can write the inequality as follows:
5 < (x/2) + 3 < 7
To find the range in which the number lies, we can set up an inequality based on the given information.
Let's represent the unknown number as "x."
According to the question, the number is halved and then increased by 3. Mathematically, this can be written as (x/2) + 3.
The result is given to be between 5 and 7. We can set up the following inequality based on this information:
5 < (x/2) + 3 < 7
To simplify this inequality, we can subtract 3 from all parts of the equation:
5 - 3 < (x/2) < 7 - 3
This simplifies to:
2 < (x/2) < 4
To remove the fraction, we can multiply all parts of the inequality by 2:
2 * 2 < x < 4 * 2
This further simplifies to:
4 < x < 8
Thus, the number lies between 4 and 8. The inequality representing this range is 4 < x < 8.