Question - Absolute Value Inequality Solution
Solution:
The inequality is $$ 3|d| + 5 < 47 $$.First, we'll isolate the absolute value expression by subtracting 5 from both sides of the inequality:$$ 3|d| + 5 - 5 < 47 - 5 $$$$ 3|d| < 42 $$Now, divide both sides by 3 to solve for the absolute value of d:$$ \frac{3|d|}{3} < \frac{42}{3} $$$$ |d| < 14 $$Since we have an absolute value inequality, we know that $$ |d| < 14 $$ means that d is less than 14 and greater than -14. Therefore, the solution set for d is:$$ -14 < d < 14 $$
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