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Which of the following values are solutions to the inequality 
4x+1 > 6?
I. 0
II. 5
III. 4
None
I only
II only
III only
I and II
I and III
II and III
I, II and III

Which of the following values are solutions to the inequality 4 x+1>6 ? \newlineI. 00\newlineII. 55\newlineIII. 44\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III

Full solution

Q. Which of the following values are solutions to the inequality 4x+1>6? 4 x+1>6 ? \newlineI. 00\newlineII. 55\newlineIII. 44\newlineNone\newlineI only\newlineII only\newlineIII only\newlineI and II\newlineI and III\newlineII and III\newlineI, II and III
  1. Solve Inequality for x: Solve the inequality for x.\newlineWe start by subtracting 11 from both sides of the inequality to isolate the term with xx.\newline4x + 1 - 1 > 6 - 1\newlineThis simplifies to:\newline4x > 5\newlineNext, we divide both sides by 44 to solve for xx.\newline\frac{4x}{4} > \frac{5}{4}\newlineThis gives us:\newlinex > \frac{5}{4}
  2. Test Value I: 00: Test the first value, I. 00. We substitute xx with 00 in the inequality x > \frac{5}{4}. 0 > \frac{5}{4} This statement is false because 00 is not greater than 54\frac{5}{4}. Therefore, I. 00 is not a solution to the inequality.
  3. Test Value II: 55: Test the second value, II. 55. We substitute xx with 55 in the inequality x > \frac{5}{4}. 5 > \frac{5}{4} This statement is true because 55 is greater than 54\frac{5}{4}. Therefore, II. 55 is a solution to the inequality.
  4. Test Value III: 44: Test the third value, III. 44. We substitute xx with 44 in the inequality x > \frac{5}{4}. 4 > \frac{5}{4} This statement is true because 44 is greater than 54\frac{5}{4}. Therefore, III. 44 is a solution to the inequality.
  5. Combine Solutions: Combine the results from Steps 22, 33, and 44 to determine which values are solutions.\newlineFrom the previous steps, we have determined that:\newlineI. 00 is not a solution.\newlineII. 55 is a solution.\newlineIII. 44 is a solution.\newlineTherefore, the values that are solutions to the inequality are II and III.

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