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Question

Find the number of integers in the solution set of |4x+3|<8.

A
None
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B
Two
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C
Three
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D
Four
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E
Infinitely many
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Solution

The correct option is D Four
Rule is when |y|<a
a<y<a
Now when |4x+3|<8, then
8<4x+3<8
Subtracting 3 from the inequality, we get
83<4x<83
11<4x<5
2.75<x<1.25
So, x has 4 possible integer values: 2,1,0,1.

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