How do you solve and graph the compound inequality #-16 < -3x + 8 < -7# ?
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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To solve the compound inequality -16 < -3x + 8 < -7, follow these steps:
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Subtract 8 from all parts of the compound inequality: -16 - 8 < -3x + 8 - 8 < -7 - 8 -24 < -3x < -15
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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
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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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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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