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

Dec 27, 2017

$x \in \left(- \infty , - \frac{11}{2}\right] \bigcup \left[4 , \infty\right)$

#### Explanation:

First Method: Rewrite as quadratic function

(4x+3)^2≥19^2

16x^2+24x-352≥0

2x^2+3x-44≥0

${x}_{1 , 2} = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

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

$x \in \left(- \infty , - \frac{11}{2}\right] \bigcup \left[4 , \infty\right)$

Second Method:

|4x+3|≥19

$4 {x}_{1} + 3 = 19$
$4 {x}_{1} = 16$
${x}_{1} = 4$

$- \left(4 {x}_{2} + 3\right) = 19$
$- 4 {x}_{2} - 3 = 19$
$- 4 {x}_{2} = 22$
${x}_{2} = \frac{22}{-} 4 = - \frac{11}{2}$

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