Question

Solve the inequality.

4-2r-14 > 0
A) r>-24
B) r<32
C) r<-24
D) r> 32

Answer 1

The inequality 4 - 2r - 14 > 0 simplifies to r < -5, but none of the given options match the correct solution, suggesting an error in the provided options.

Step-by-step explanation:

To solve the inequality 4 - 2r - 14 > 0, we must first simplify the inequality by combining like terms.

4 - 14 = -10, so the inequality becomes:

-2r - 10 > 0

Next, we add 10 to both sides of the inequality:

-2r > 10

Now we divide both sides by -2, remembering to flip the inequality sign because we are dividing by a negative number:

r < -5

Therefore, the solution to the inequality 4 - 2r - 14 > 0 is r < -5.

However, none of the given options A) r > -24, B) r < 32, C) r < -24, D) r > 32 match the correct solution, which implies there may have been an issue with the question or the provided options.