Answer:
x > 2/3 or x < -10/3
Step-by-step explanation:
|3x + 4| > 6
To solve an absolute value inequality of the form |X| > b, where X is an expression, and b is a number, change the inequality into this compound inequality:
X > b or X < -b
Here, X is 3x + 4.
b is 6.
We get the compound inequality:
3x + 4 > 6 or 3x + 4 < -6
3x > 2 or 3x + 4 < -6
x > 2/3 or 3x < -10
x > 2/3 or x < -10/3
Answer:
[tex]\left(- \infty, -\dfrac{10}{3}\right) \cup \left(\dfrac{2}{3}, \infty\right)[/tex]
Step-by-step explanation:
To solve an inequality containing an absolute value:
Given inequality:
[tex]|3x+4| > 6[/tex]
Apply the absolute rule:
[tex]\textsf{If }\:|u| > a,\:a > 0\:\textsf{ then }\:u < -a \:\textsf{ or }\: u > a[/tex]
Therefore:
[tex]\begin{aligned}\text{\underline{Case 1}} && \text{\underline{Case 2}}\\3x+4 & < -6 \quad & 3x+4 & > 6\\3x & < -10 \quad & 3x & > 2\\x & < -\dfrac{10}{3} \quad & x & > \dfrac{2}{3}\end{aligned}[/tex]
So the solution to the inequality in interval notation is:
[tex]\left(- \infty, -\dfrac{10}{3}\right) \cup \left(\dfrac{2}{3}, \infty\right)[/tex]
