suppose that y=5x+1 and we want y to be within 0.04 unit of 9. for what values of x will this be true?

1.592 < x < 1.608

So x must be between 1.592 and 1.608

Step-by-step explanation:

y=5x+1

Since we know that y must be within. 04 of 9, we know the highest y value will be 9 +.04 = 9.04, and the lowest y value will be 9 -.04 = 8.96

We can write this as an inequality like such:

8.96 < y < 9.04

So we need to find where y is greater than 8.96, and less than 9.04

To do this we need to solve both equations for x

9.04 = 5x + 1

8.04 = 5x

8.04/5 = x

1.608 = x

So we know when x = 1.608 then y = 9.04

Now lets solve for the smaller y value

8.96 = 5x + 1

7.96 = 5x

7.96/5 = x

1.592 = x

So we know when x = 1.592 then y = 8.96

So y will be between 9.04 and 8.96 from 1.592 to 1.608

The range must be between:

1.592 < x < 1.608