Question

If 2x + 5 ≤ 9, what is the greatest possible value of
2x - 5 ?

Answer 1

-1

Explanation:

Since we have the linear equation, 2x-5, and it's increasing since the slope is positive, that means we want the maximum x-value, to find the maximum y-value, or possible value.

This means, we want to find the maximum x-value of 2x+5 that is less than or equal to 9, and since we want the maximum x-value, we want the right side to also be the maximum, and since we have a less than or equal to symbol, we can have the equation equal to 9, which is the make value. So we get the following equation

`2x+5=9\\`

Subtract 9 from both sides

`2x=4`

Divide both sides by 2

`x=2`

This is the maximum x-value we can get from the inequality, and now we plug this into the equation 2x-5

`2(2)-5`

4-1

-1

So the maximum value is -1