Question - Solving Absolute Value Inequality and Writing as a Compound Inequality
Solution:
To solve the inequality $$ 4|v - 3| \leq 28 $$ and write it as a compound inequality, follow these steps:1. First, isolate the absolute value on one side by dividing both sides of the inequality by 4:\[ |v - 3| \leq \frac{28}{4} \]\[ |v - 3| \leq 7 \]2. Now, remember that the absolute value inequality $$ |x| \leq a $$ can be written as the compound inequality $$ -a \leq x \leq a $$. Applying this to your inequality, you get:\[ -7 \leq v - 3 \leq 7 \]3. Adding 3 to all parts of the compound inequality to solve for $$ v $$ gives us:\[ -7 + 3 \leq v - 3 + 3 \leq 7 + 3 \]\[ -4 \leq v \leq 10 \]So, the solution to the inequality $$ 4|v - 3| \leq 28 $$ expressed as a compound inequality is $$ -4 \leq v \leq 10 $$.
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