If 4x + 1 > 2x + 5, what is the minimum integer value of x?

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Question: If 4x + 1 > 2x + 5, what is the minimum integer value of x?

Options:

Correct Answer: 3

Solution:

Solving gives 2x > 4, thus x > 2. The minimum integer is 3.

If 4x + 1 > 2x + 5, what is the minimum integer value of x?

If 4x + 1 > 2x + 5, what is the minimum integer value of x?

Step 1: Start with the inequality: 4x + 1 > 2x + 5.
Step 2: Subtract 2x from both sides to simplify: 4x - 2x + 1 > 5.
Step 3: This simplifies to: 2x + 1 > 5.
Step 4: Now, subtract 1 from both sides: 2x > 5 - 1.
Step 5: This simplifies to: 2x > 4.
Step 6: Next, divide both sides by 2: x > 4 / 2.
Step 7: This simplifies to: x > 2.
Step 8: The question asks for the minimum integer value of x that satisfies this inequality.
Step 9: The smallest integer greater than 2 is 3.

Inequalities – Understanding how to manipulate and solve inequalities to find variable ranges.
Integer Values – Identifying the smallest integer that satisfies the given inequality.