Question

Which expressions, written to the right of the equals sign, would complete this equation so that it has one solution? 4(2x – 3) – 4x = Choose exactly two answers that are correct. A. 4x – 12 B. 3x – 4 C. 3(2x – 6) D. 4(x – 5)

Answer 1

The expression 4(2x – 3) – 4x is equal to 4·2x-4·3-4x=8x-12-4x=(8x-4x)-12=4x-12.

1. 4x-12=4x-12, then 0=0. This equation has infinite amount of solutions;
2. 4x-12=3x-4,4x-3x=-4+12,x=8. This equation has one solution.
3. 4x-12=3(2x-6),4x-12=6x-18,4x-6x=-18+12,-2x=-6,x=3. This equation also has one solution.
4. 4x-12=4(x-5),4x-12=4x-20,4x-4x=-20+12,0=-8 is not right equality, then this equation hasn't solutions.
Answer: Correct choices are B and C.