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Solve for a: 1/9*|5a + 2| < 1. Express your answer in interval notation.

 Jan 30, 2022
 #1
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First, let's simplify it: 

 

|5a + 2| < 9

 

For an absolute value inequality, you split it into two - one is positive and the other is negative. (Remember to flip the sign in the negative one!)

 

5a + 2 < 9

&

5a + 2 > -9

 

For the first one: 

 

5a < 7

a < 7/5

 

For the second one: 

 

5a > -11

a > -11/5

 

Thus we have our range: -11/5 < a < 7/5

 

Therefore, in interval notation, our answer is (-11/5, 7/5).

 

⚡⚡⚡

ShockFish

 Jan 30, 2022

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