Math Problem Statement
Solve the absolute value equation |x - 8| + 1 = 6.
Solution
The equation given in the image is:
Let's solve this step by step:
Step 1: Isolate the absolute value expression.
Subtract 1 from both sides of the equation:
Step 2: Set up two cases for the absolute value equation.
By definition, means that either or .
Case 1:
Case 2:
Step 3: Final solution
The solutions are:
Would you like more details on any step?
Here are 5 related questions to further your understanding:
- What does the absolute value function represent geometrically?
- How do you solve absolute value inequalities?
- What happens if an absolute value equation has no solution?
- How can you graph the solutions to this equation on a number line?
- Can you create an absolute value equation that has only one solution?
Tip: Always isolate the absolute value expression first when solving such equations.
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Math Problem Analysis
Mathematical Concepts
Absolute Value Equations
Linear Equations
Formulas
|x - a| = b
x - a = b or x - a = -b
Theorems
Properties of Absolute Value
Suitable Grade Level
Grades 6-8