Question

Solve the inequality -13(r+5) + 25 > 4(r-10).

a. r < 5
b. r > -5
c. r < -5
d. r > 5

Answer 1

To solve the inequality -13(r+5) + 25 > 4(r-10), distribute numbers inside the brackets, combine like terms, and solve for r to find that r must be less than 0, which is not explicitly listed in the options provided.

Step-by-step explanation:

To solve the inequality -13(r+5) + 25 > 4(r-10), follow these steps:

1. Distribute the -13 into the parenthesis: -13 * r - 65 + 25 > 4 * r - 40.
2. Simplify the terms: -13r - 40 > 4r - 40.
3. Add 13r to both sides to get all r terms on one side and simplify: -40 > 17r - 40.
4. Add 40 to both sides to isolate the r term: 0 > 17r.
5. Divide both sides by 17 to solve for r: r < 0.

This solution shows that r must be less than 0. Therefore, looking at the options provided, none of them are correct since they state numbers greater than or equal to -5 or 5. The inequality simplifies to r < 0, which states that r is any negative number.