Math Problem Statement
|10-4y| ≥ 4
Solution
We are given the inequality:
Step 1: Understand the absolute value inequality
For absolute value inequalities of the form , where , we split it into two cases:
So, applying this to our equation:
Step 2: Solve each inequality separately
Case 1:
Subtract 10 from both sides: Now, divide by (remember to reverse the inequality when dividing by a negative number): So, .
Case 2:
Subtract 10 from both sides: Now, divide by (again, reverse the inequality): So, .
Step 3: Combine the results
From Case 1, we have , and from Case 2, we have .
Thus, there is no overlap between these two conditions, so the solution to the inequality is:
Final Solution:
Would you like further details on any step?
Here are 5 related questions:
- How do you solve absolute value equations instead of inequalities?
- What happens when the absolute value inequality has a strict inequality, like ?
- Can you explain how to graph absolute value inequalities on a number line?
- What is the difference between "and" & "or" conditions in absolute value inequalities?
- How would this solution change if the inequality was ?
Tip: Always remember to flip the inequality when dividing or multiplying by a negative number!
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Math Problem Analysis
Mathematical Concepts
Absolute Value Inequalities
Inequalities
Linear Equations
Formulas
For |A| ≥ B, where B ≥ 0: A ≥ B or A ≤ -B
Theorems
Absolute Value Theorem
Suitable Grade Level
Grades 8-10