Question - Solving Inequalities Involving Absolute Value
Solution:
To solve the inequality $$-9|c| < -50$$, let's start by isolating the absolute value term.Firstly, divide both sides by -9 to get the absolute value by itself. It's important to remember that when we divide or multiply both sides of an inequality by a negative number, the direction of the inequality symbol changes. So the inequality will reverse in this case.$$-9|c| < -50 \quad / :(-9)$$$$|c| > \frac{-50}{-9}$$$$|c| > \frac{50}{9}$$Since the absolute value of a number is always nonnegative, we can write this as two separate inequalities:$$c > \frac{50}{9} \quad or \quad c < -\frac{50}{9}$$So the solution to the inequality is that $$c$$ is either greater than $$\frac{50}{9}$$ or less than $$-\frac{50}{9}$$.
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