Question

Which is the solution to the inequality?

1.) 1/4 + x < 5/6
2.) x < 7/12
3.) x > 7/12
4.) x < 1 and 1/12
5.) x > 1 and 1/12

Answer 1

To solve 1/4 + x < 5/6, subtract 1/4 from both sides and find a common denominator to get x < 7/12, making option 2, x < 7/12, the correct solution to the inequality.

Step-by-step explanation:

The student has asked for the solution to the inequality 1/4 + x < 5/6. To solve this inequality, we must first isolate the variable x on one side. Starting with the inequality:

• 1/4 + x < 5/6,

we subtract 1/4 from both sides to get:

• x < 5/6 - 1/4.

To subtract these fractions, they must have a common denominator. Multiplying 1/4 by 3/3 to get 3/12, and 5/6 by 2/2 to get 10/12, we find:

• x < 10/12 - 3/12,
• x < 7/12.

So, the correct solution to the inequality is option 2: x < 7/12.