2. Linear Equations and Inequalities

Absolute Value Inequalities

2. Linear Equations and Inequalities

Absolute Value Inequalities

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Multiple Choice

Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(B) $3 ∣ 2 x + 5 ∣ + 3 < 12$

$\left(-4,-1\right)$

Number line from -8 to 8 with red parentheses highlighting the interval between -3 and -1.

$\left(1,4\right)$

$\left\lbrack1,4\right\rbrack$

Number line from -8 to 8 with the interval between 2 and 4 highlighted in red brackets.

$\left\lbrack-4,-1\right\rbrack$

Number line from -8 to 8 with the interval from -3 to -1 highlighted in red brackets.

Verified step by step guidance

Start with the given inequality: \$3\left|2x + 5\right| + 3 < 12$.

Isolate the absolute value expression by subtracting 3 from both sides: \$3\left|2x + 5\right| < 12 - 3$.

Simplify the right side: \$3\left|2x + 5\right| < 9$.

Divide both sides by 3 to further isolate the absolute value: $\left|2x + 5\right| < \frac{9}{3}$.

Simplify the fraction: $\left|2x + 5\right| < 3$. Now, rewrite this absolute value inequality as a compound inequality without absolute value: $-3 < 2x + 5 < 3$.

5:54m

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Struggling with Intermediate Algebra?

Solve and graph the following absolute value inequalities. Express the solution in interval notation.(B) 3∣2x+5∣+3<123\left|2x+5\right|+3<12

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Solve and graph the following absolute value inequalities. Express the solution in interval notation.
(B) $3 ∣ 2 x + 5 ∣ + 3 < 12$