Math Problem Statement

The solution of the inequality |x| ≤ 7 is the following interval. (Enter your answer using interval notation.)

Solution

The inequality x7|x| \leq 7 means that the absolute value of xx is less than or equal to 7. This can be rewritten as:

7x7-7 \leq x \leq 7

Therefore, the solution in interval notation is:

[7,7][-7, 7]

Would you like further details or have any questions?

Here are 5 related questions you might find interesting:

  1. How would the interval change if the inequality was x<7|x| < 7?
  2. What is the solution to x7|x| \geq 7 in interval notation?
  3. How do you solve inequalities with absolute values involving a variable on both sides, such as x+35|x + 3| \leq 5?
  4. What is the graphical representation of the solution to x7|x| \leq 7?
  5. How does the interval notation change if you replace the inequality with x>7|x| > 7?

Tip: Always remember that solving absolute value inequalities involves considering both the positive and negative scenarios for the expression inside the absolute value.

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Absolute Value

Formulas

|x| ≤ a ⟶ -a ≤ x ≤ a

Theorems

Absolute Value Inequality Theorem

Suitable Grade Level

Grades 6-8