Determine whether each value of x is a solution of the inequality. Inequality |x-10| ≥3 Values (

Step 1: First, we need to understand what the absolute value inequality $|x-10| geq 3$ means. Th

Determine whether each value of x is a solution of the...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solution Verification

Once an inequality is solved in general, substituting specific values into the inequality helps determine whether those values meet the condition specified by the inequality. This method is crucial for checking if a given number is within the solution set.

Compound Inequalities

When solving an absolute value inequality like |x - a| ? b, it is equivalent to solving two separate inequalities: x - a ? b or x - a ? -b. This compound inequality approach captures all x that satisfy the original inequality.

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. This concept is fundamental when dealing with expressions like |x - a|, which represents the distance between x and a.

Absolute Value Inequalities

Inequalities involving absolute values, such as |x - a| ? b, require considering the definition of absolute value to split the inequality into two cases. This ensures that the distance from x to a is at least b, covering both x values less than a - b and greater than a + b.

Please give Ace some feedback