How do you solve and graph the compound inequality #-16 < -3x + 8 < -7# ?

Answer 1

Subtract 8 from the compound inequality -16< -3x +8< -7, to have

-24<-3x<-15. Now divide it by 3 to have

-8<-x<-5

8>x>5 is thus the required solution.

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Answer 2

To solve the compound inequality -16 < -3x + 8 < -7, follow these steps:

  1. Subtract 8 from all parts of the compound inequality: -16 - 8 < -3x + 8 - 8 < -7 - 8 -24 < -3x < -15

  2. Divide all parts of the compound inequality by -3. Since you're dividing by a negative number, flip the direction of the inequality signs: (-24) / (-3) > (-3x) / (-3) > (-15) / (-3) 8 > x > 5

  3. Graph the solution on a number line. Draw an open circle at 8 and another open circle at 5 to represent that the solutions are not inclusive of these points. Then shade the region between 8 and 5 to represent the values of x that satisfy the compound inequality.

Final graph: -------o-------------------o------- 5 8

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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