How do you graph and solve |4x + 3| ≥ 19?

1 Answer
Dec 27, 2017

x in (-oo,-11/2]uuu[4,oo)

Explanation:

First Method: Rewrite as quadratic function

(4x+3)^2≥19^2

16x^2+24x-352≥0

2x^2+3x-44≥0

x_(1,2)=(-b+-sqrt(b^2-4ac))/(2a)

=>x_(1,2)=4; -11/2

x in (-oo,-11/2]uuu[4,oo)

Second Method:

|4x+3|≥19

4x_1+3=19
4x_1=16
x_1=4

-(4x_2+3)=19
-4x_2-3=19
-4x_2=22
x_2=22/-4=-11/2

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(I personally prefer first method eventhough it is more difficult. I can tell the interval in a second)