Math Problem Statement
The problem below was solved incorrectly. Identify the error and the correct solution: 4 + 3(2x - 3) ≥ 4x + 5.
Solution
Let's carefully analyze the problem and identify the error.
The original inequality is:
Step-by-step breakdown:
- Distribute the 3 in :
- Combine like terms on the left-hand side:
- Move to the left-hand side by subtracting from both sides: Simplifying gives:
- Add 5 to both sides:
- Divide both sides by 2:
Identifying the mistake:
The solution in the image shows:
which is incorrect. The correct inequality should be:
Answer:
The correct choice is:
- The correct answer is ; the person combined , which are not like terms.
Do you want more details or have any other questions?
Related questions:
- Why is it important to combine like terms carefully in inequalities?
- How do you reverse the inequality symbol when dividing by a negative number?
- What are common mistakes to avoid when solving inequalities?
- How can you check your solution to an inequality?
- What happens to the inequality sign when multiplying or dividing by a negative number?
Tip:
Always verify each step carefully in inequalities, especially when dealing with distributing, combining terms, and reversing inequality signs.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Distributive Property
Combining Like Terms
Formulas
ax + b ≥ cx + d
Theorems
Inequality Properties
Suitable Grade Level
Grades 7-9