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.
(A) $∣ 10 x - 4 ∣ - 2 > - 8$

No solution

$\left(-0.2,1\right)$

Number line from -8 to 8 with an open interval between 0 and 1 marked in red parentheses.

$x<-0.2$ OR $x>1$

Number line graph showing the solution to the absolute value inequality |10x - 4| - 2 > -8 with excluded points at 1 and 2.

All real Numbers

Number line from -8 to 8 with red arrows at both ends and labeled x-axis for graphing inequalities.

Verified step by step guidance

Start with the given inequality: $\left|10x - 4\right| - 2 > -8$.

Isolate the absolute value expression by adding 2 to both sides: $\left|10x - 4\right| > -8 + 2$.

Simplify the right side: $\left|10x - 4\right| > -6$.

Recall that the absolute value of any expression is always greater than or equal to 0, so $\left|10x - 4\right|$ is always greater than -6. This means the inequality holds for all real values of $x$.

Conclude that the solution set is all real numbers, and when graphing, represent this by shading the entire number line.

5:54m

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Struggling with Intermediate Algebra?

Solve and graph the following absolute value inequalities.(A) ∣10x−4∣−2>−8\left|10x-4\right|-2>-8

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Solve and graph the following absolute value inequalities.
(A) $∣ 10 x - 4 ∣ - 2 > - 8$