Example Card: Solving a Basic Absolute-Value Equation
Solve basic absolute value equations step by step by splitting into positive and negative cases. Practice Grade 9 absolute value problem-solving with worked examples.
Key Concepts
An absolute value equation often hides two different solutions in plain sight. Let's practice solving one by splitting it into two separate cases.
Example Problem Solve the equation $|x+5| = 12$.
Step by Step 1. Using the definition of absolute value, we can write $|x+5| = 12$ as two separate equations. 2. Case 1: The expression inside the absolute value is positive. $$x+5 = 12$$ 3. Subtract 5 from both sides to solve for $x$. $$x = 7$$ 4. Case 2: The expression inside the absolute value is negative. $$x+5 = 12$$ 5. Subtract 5 from both sides to solve for $x$. $$x = 17$$ 6. The solution set contains both values we found. $$\{7, 17\}$$.
Common Questions
What are the key steps to solving a basic absolute-value equation?
Identify the equation type, isolate the variable using inverse operations, and verify by substituting back into the original equation.
What common mistakes occur when solving a basic absolute-value equation?
Applying operations to only one side, sign errors when moving terms, and not checking solutions in the original equation.
How is this skill applied in real problems?
These techniques model physical, financial, and geometric situations where unknown quantities must be found from given conditions.