Question - Solving Absolute Value Inequalities
Solution:
To solve the inequality $$ |c| - 1 \geq 11 $$, you need to isolate the absolute value on one side of the inequality.First, add 1 to both sides of the inequality:\[ |c| - 1 + 1 \geq 11 + 1 \]\[ |c| \geq 12 \]The absolute value $$ |c| $$ represents the distance from 0 on the number line, and it can be either positive or negative. Since $$ |c| \geq 12 $$, this means that c can either be greater than or equal to 12, or less than or equal to -12.Split the inequality into two cases:1. $$ c \geq 12 $$ (when c is positive or zero)2. $$ c \leq -12 $$ (when c is negative)Therefore, the solution set for $$ |c| - 1 \geq 11 $$ is $$ c \geq 12 $$ or $$ c \leq -12 $$.
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