Question

HELPPPP

Mr. Hagan writes an equation on the board.

8k−14=−4k+10+12(k−2)
Which statement is true about Mr. Hagan’s equation when solving for k?

A. The equation has exactly one solution.

B. The equation has exactly two solutions.

C. The equation has infinitely many solutions.

D. The equation has zero solutions.

Answer 1

C - this equation is simplified to a numeric identity. the variable has infinite solutions.

8k - 14 = -4k + 10 + 12(k - 2) --> use distributive property

8k - 14 = -4k + 10 + 12k -24 --> combine like terms

8k - 14 = 8k -14 --> combine like to each side

8k - 8k = -14 + 14 --> simplify

0 = 0

note, the variable cancels out, therefore there is no identity and ANY numeroc value can be used, as ant value will cancel itself out.

this means there is an infinite numbers of solutions.