Problem 62 - College Algebra Essentials

Question

Solve each absolute value inequality. $$|x+3| \leq 4$$

Step-by-Step Solution

Answer

The solution to the inequality \(|x+3| \leq 4\) is \(-7 \leq x \leq 1\).

Step 1: Identify Inequality

Here, you can see that the inequality is \(|x+3| \leq 4\)

Step 2: Apply Absolute Value Inequality Definition

According to the definition of absolute value, the equation \(|x+3| \leq 4\) is equivalent to \(-4 \leq x+3 \leq 4\).

Step 3: Solve for 'x'

Now, you can solve the inequality \(-4 \leq x + 3 \leq 4\) for 'x'. This will involve subtracting 3 from all parts of the inequality, which will give you \(-4 - 3 \leq x \leq 4 - 3\), simplifying to \(-7 \leq x \leq 1\).