Question

I am very confused, please help!

Answer 1

D

Explanation:

Consider the equation:

`(3)/(4)(24-16x)=-(2)/(3)(18x-27)`

Use distributive property in both sides:

`(3)/(4)\cdot 24-(3)/(4)\cdot 16x=-(2)/(3)\cdot 18x+(2)/(3)\cdot 27\\ \\3\cdot 6-3\cdot 4x=-2\cdot 6x+2\cdot 9\\ \\18-12x=-12x+18`

Separate terms with x into the left part and terms without x into the right part:

`-12x+12x=18-18\\ \\0=0`

Since you get true equality 0 = 0, the equation is true for all real values of x. So, the equation has infinitely many solutions.