Solving Absolute Value Inequality
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.
