Final answer:
The solution set for the inequality 1/4x-3 < 2/3x+7 is x > -24. This is obtained by isolating x and simplifying the inequality step by step. Option d. x>-24 is the correct answer.
Explanation:
The student's question of finding the solution set for 1/4x-3 < 2/3x+7 involves solving a linear inequality, which is a basic concept in algebra. To find the solution, let's first isolate the variable x on one side of the inequality.
- Subtract 1/4x from both sides: -3 < 2/3x - 1/4x + 7.
- Find a common denominator and combine like terms: -3 < (8/12x - 3/12x) + 7.
- Simplify the inequality: -3 < 5/12x + 7.
- Subtract 7 from both sides: -10 < 5/12x.
- Multiply both sides by 12/5 to solve for x: -24 < x.
This means that the solution set for the inequality is x > -24, which corresponds to option (d).