Math Problem Statement
Solution
The problem is asking to solve the inequality for :
where .
Let's break it down:
Step 1: Expand the inequality
Expand the left-hand side: So the inequality becomes:
Step 2: Move terms involving to one side
Subtract from both sides:
Step 3: Factor the right-hand side
The right-hand side can be factored as:
Step 4: Solve for
Now, divide both sides by (since and , we know , so the direction of the inequality remains the same):
Step 5: Check answer options
From the options given in the image, the correct answer corresponds to: which matches the first option.
Final Answer:
The correct option is the first one:
Do you have any questions or would you like more details on any step?
Here are 5 related questions to deepen your understanding:
- How would the inequality change if or were negative?
- What happens to the solution if ?
- How does solving inequalities differ from solving equalities?
- Can you generalize this method for other inequalities involving linear expressions?
- How would the steps differ if the inequality symbol was instead of ?
Tip: When solving inequalities, always pay attention to the direction of the inequality, especially when multiplying or dividing by negative numbers.
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Math Problem Analysis
Mathematical Concepts
Inequalities
Linear Algebra
Formulas
a(bx + c) ≥ bc
abx + ac ≥ bc
x ≥ c(b-a) / ab
Theorems
Basic properties of inequalities
Factoring and expanding linear expressions
Suitable Grade Level
Grades 10-12