Question

Solve: |2x + 3| -1 < 4

Answer 1

|2x+3|-1<4
|2x+3|<5

1) when 2x +3 is positive
2x+3<5
2x<2
x<1 (-∞, 1)

2) when 2x+3 is negative
-(2x+3)<5
-2x-3<5
-2x<8
x>-4 (-4, ∞)

(-∞, 1)∩(-4, ∞)=(-4,1)

Answer 2

Add 1
|2x +3| < 5
Unfold
-5 < 2x +3 < 5
Subtract 3
-8 < 2x < 2
Divide by 2
-4 < x < 1

The solution is
-4 < x < 1

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If you subtract 4 from both sides, you get an expression that compares to zero. Most graphing calculators will show you the zero-crossings, so you can easily find the values of x where this is true.