Math Problem Statement

Solve the following equation: 9 = |3x|

Solution

The equation shown in the image is 9=3x9 = |3x|. Let's solve this step by step.

Step 1: Break down the absolute value equation.

The equation 9=3x9 = |3x| implies two possible equations:

  1. 3x=93x = 9
  2. 3x=93x = -9

Step 2: Solve both equations.

  1. For 3x=93x = 9: x=93=3x = \frac{9}{3} = 3

  2. For 3x=93x = -9: x=93=3x = \frac{-9}{3} = -3

Final Solution:

The solutions are x=3x = 3 and x=3x = -3.

Would you like further details or clarification on this? Here are 5 related questions you might find useful:

  1. How do you solve absolute value inequalities?
  2. Can you explain the concept of absolute value in more depth?
  3. How would the equation change if the constant was negative instead of positive?
  4. What happens if there's no solution to an absolute value equation?
  5. How do you graph solutions of absolute value equations?

Tip: When solving absolute value equations, always split the equation into two cases—one where the expression inside the absolute value is positive and one where it's negative.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value
Linear Equations

Formulas

|Ax| = B implies Ax = B or Ax = -B

Theorems

Properties of Absolute Value

Suitable Grade Level

Grade 7-9