Question

question
solve the following inequality algebraically.
|x - 3| < 10

Explanation:

Step1: Apply absolute value inequality rule

For $|A| < b$ where $b>0$, this translates to $-b < A < b$. Here, $A = x-3$ and $b=10$, so:
$$-10 < x - 3 < 10$$

Step2: Add 3 to all three parts

Isolate $x$ by adding 3 to each segment of the inequality:
$$-10 + 3 < x - 3 + 3 < 10 + 3$$

Step3: Simplify all expressions

Calculate each term to find the range of $x$:
$$-7 < x < 13$$

Answer:

$-7 < x < 13$