Determine whether each value of x is a solution of the...

Determine whether each value of $x$ is a solution of the inequality. (Values) (a) $x=3 \quad$ (b) $x=-3$ (c) $x=\frac{5}{2} \quad$ (d) $x=\frac{3}{2}$ (a) $x=-\frac{1}{2} \quad$ (b) $x=-\frac{5}{2}$ (c) $x=\frac{4}{3} \quad$ (d) $x=0$ (a) $x=-1 \quad$ (b) $x=\sqrt{5}$ (c) $x=1 \quad$ (d) $x=5$ (a) $x=13 \quad$ (b) $x=-1$ (c) $x=14 \quad$ (d) $x=8$ $$|x-10| \geq 3$$

Determine whether each value of $x$ is a solution of the inequality.
(Values)
(a) $x=3 \quad$ (b) $x=-3$
(c) $x=\frac{5}{2} \quad$ (d) $x=\frac{3}{2}$
(a) $x=-\frac{1}{2} \quad$ (b) $x=-\frac{5}{2}$
(c) $x=\frac{4}{3} \quad$ (d) $x=0$
(a) $x=-1 \quad$ (b) $x=\sqrt{5}$
(c) $x=1 \quad$ (d) $x=5$
(a) $x=13 \quad$ (b) $x=-1$
(c) $x=14 \quad$ (d) $x=8$
$$|x-10| \geq 3$$

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Key Concepts

Absolute Value

The absolute value of a number represents its non-negative distance from zero on the number line. It is a measure of magnitude without regard to direction, which forms the basis for understanding expressions involving absolute values.

Absolute Value Inequalities

Absolute value inequalities, such as those of the form |x - a| ? b, set conditions on the distance between x and a. These inequalities are interpreted as compound inequalities, resulting in two separate conditions: x - a ? b or x - a ? -b. This concept is crucial for determining the solution set of the inequality.

Solution Verification by Substitution

Verifying candidate solutions by substitution involves plugging each proposed value into the inequality to check if it satisfies the given condition. This method is fundamental in determining whether individual numbers belong to the solution set of the inequality.

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