Math Problem Statement
-5∣5x−1∣−6= −41
Solution
We are given the equation:
Step 1: Isolate the absolute value term
We first add 6 to both sides:
Step 2: Divide both sides by -5
To isolate the absolute value expression, divide both sides by -5:
Step 3: Solve the absolute value equation
The expression has two cases:
Case 1:
Add 1 to both sides: Divide by 5:
Case 2:
Add 1 to both sides: Divide by 5:
Final Solution:
The solutions are:
Would you like any further details or explanations?
Here are five related questions for practice:
- Solve .
- Solve .
- What is the general process for solving absolute value equations?
- How does isolating the absolute value term help in solving such equations?
- What happens when an absolute value equation has no solution?
Tip: When solving absolute value equations, always remember to split the equation into two cases—one for the positive and one for the negative scenario!
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Math Problem Analysis
Mathematical Concepts
Algebra
Absolute Value Equations
Linear Equations
Formulas
Absolute value equation: |Ax + B| = C
Linear equation: Ax + B = C
Theorems
Absolute value equation solving method
Suitable Grade Level
Grades 8-10