Question

I am very confused, please help!

Answer 1

Answer:

D

Step-by-step explanation:

Consider the equation:

$\dfrac{3}{4}(24-16x)=-\dfrac{2}{3}(18x-27)$

Use distributive property in both sides:

$\dfrac{3}{4}\cdot 24-\dfrac{3}{4}\cdot 16x=-\dfrac{2}{3}\cdot 18x+\dfrac{2}{3}\cdot 27\\ \\3\cdot 6-3\cdot 4x=-2\cdot 6x+2\cdot 9\\ \\18-12x=-12x+18$

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.