Which of the following values are solutions to the inequality 4 x+1>6 ? I. 0II. 5III. 4NoneI onlyII onlyIII onlyI and III and IIIII and IIII, II and III
Q. Which of the following values are solutions to the inequality 4x+1>6?I. 0II. 5III. 4NoneI onlyII onlyIII onlyI and III and IIIII and IIII, II and III
Solve Inequality for x: Solve the inequality for x.We start by subtracting 1 from both sides of the inequality to isolate the term with x.4x + 1 - 1 > 6 - 1This simplifies to:4x > 5Next, we divide both sides by 4 to solve for x.\frac{4x}{4} > \frac{5}{4}This gives us:x > \frac{5}{4}
Test Value I: 0: Test the first value, I. 0. We substitute x with 0 in the inequality x > \frac{5}{4}. 0 > \frac{5}{4} This statement is false because 0 is not greater than 45. Therefore, I. 0 is not a solution to the inequality.
Test Value II: 5: Test the second value, II. 5. We substitute x with 5 in the inequality x > \frac{5}{4}. 5 > \frac{5}{4} This statement is true because 5 is greater than 45. Therefore, II. 5 is a solution to the inequality.
Test Value III: 4: Test the third value, III. 4. We substitute x with 4 in the inequality x > \frac{5}{4}. 4 > \frac{5}{4} This statement is true because 4 is greater than 45. Therefore, III. 4 is a solution to the inequality.
Combine Solutions: Combine the results from Steps 2, 3, and 4 to determine which values are solutions.From the previous steps, we have determined that:I. 0 is not a solution.II. 5 is a solution.III. 4 is a solution.Therefore, the values that are solutions to the inequality are II and III.