Question - Solving Absolute Value Inequality
Solution:
The inequality in the image is written as `8|y| ≤ 24`. Here, we want to solve for the variable `y`. The term `|y|` represents the absolute value of `y`, which means it is the distance of `y` from zero on the number line and is always nonnegative.To solve the inequality for `y`, follow these steps:1. Divide both sides of the inequality by 8 to isolate the absolute value expression: $$ |y| ≤ 24 / 8 $$ $$ |y| ≤ 3 $$2. The solution to the absolute value inequality $$ |y| ≤ 3 $$ means that `y` can be any number within the interval [-3, 3], including -3 and 3.In interval notation, the solution is written as: $$ y ∈ [-3, 3] $$This interval represents all values of `y` that satisfy the original inequality.
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