Question

100 points for this one

Answer 1

x < -11 or x > 8

Explanation:

Given absolute value inequality:

`|2x+3| > 19`

`\boxed{\begin{minipage}{7.1 cm}\underline{Absolute rule}\\\\If\;\;$|u| > a,\;a > 0$\;\;then\;\;$u < -a$\;\;or\;\;$u > a$\\ \end{minipage}}`

Apply the absolute rule:

`\underline{\sf Case\;1}\\\begin{aligned}2x+3& < -19\\2x& < -22\\x& < -11\end{aligned}`
`\underline{\sf Case\;2}\\\begin{aligned}2x+3& > 19\\2x& > 16\\x& > 8\end{aligned}`

To graph the solution:

• Place open circles at -11 and 8.
• Shade to the left of the open circle at -11.
• Shade to the right of the open circle at 8.

Answer 2

• C) x < - 11 or x > 8

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First, solve the inequality:

• |2x + 3| > 19
• 2x + 3 > 19 or 2x + 3 < - 19
• 2x > 16 or 2x < - 22
• x > 8 or x < - 11

This is option C (you have chosen it correctly).

Now, graph it:

• Mark points - 11 and 8 on the number line with open circle, then shade to the left from point - 11 and to the right from point 8.