Question

Please help me fast

i Elena began to solve this equation:
12x + 6(4x + 3)
= 2(6x + 4-2)
3
12x + 6(4x + 3) = 3(2(6x + 4) - 2)
12x + 6(4x + 2) = 6(6x + 4) - 6
12.x + 24x + 18 = 36x + 24 - 6
When she got to the last line, she stopped and said the equation is true for all values of x (infinite solutions),
low could Elena tell?
A The variable terms and constant terms are different
B. The variable terms are the same, but the constant terms are different
C. The variable terms are different, but the constant terms are the same
D. The variable terms and constant terms are the same

Answer 1

A rrrrriiiiiiiiiiiigggggggggghhhhhhhhhttttttttttt

Answer 2

When Elena got to the last line, she stopped and said the equation is true for all values of x (infinite solutions), she could tell because: D. The variable terms and constant terms are the same.

In Mathematics and Geometry, an equation is said to have an infinitely many solution (infinite number of solutions) when the left hand side and right hand side of the equation are the same or equal.

Based on the steps for solving the given equation, the last line by Elena is as follows;

12x + 24x + 18 = 36x + 24 - 6

36x + 18 = 36x + 18

In this context, we can logically deduce that this equation has infinitely many solution (infinite number of solutions) because the variable terms (36x) and constant terms (18) are the same.

In conclusion, every point located on this line would satisfy the equation as they would both coincide and increase to infinity.