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:

4+3(2x3)4x+54 + 3(2x - 3) \geq 4x + 5

Step-by-step breakdown:

  1. Distribute the 3 in 3(2x3)3(2x - 3): 4+6x94x+54 + 6x - 9 \geq 4x + 5
  2. Combine like terms on the left-hand side: 6x54x+56x - 5 \geq 4x + 5
  3. Move 4x4x to the left-hand side by subtracting 4x4x from both sides: 6x4x556x - 4x - 5 \geq 5 Simplifying gives: 2x552x - 5 \geq 5
  4. Add 5 to both sides: 2x102x \geq 10
  5. Divide both sides by 2: x5x \geq 5

Identifying the mistake:

The solution in the image shows:

x73x \geq \frac{7}{3}

which is incorrect. The correct inequality should be:

x5x \geq 5

Answer:

The correct choice is:

  • The correct answer is x5x \geq 5; the person combined 4+6x4 + 6x, which are not like terms.

Do you want more details or have any other questions?

Related questions:

  1. Why is it important to combine like terms carefully in inequalities?
  2. How do you reverse the inequality symbol when dividing by a negative number?
  3. What are common mistakes to avoid when solving inequalities?
  4. How can you check your solution to an inequality?
  5. 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