Question

Does 4(5x+3)-9x=11x+12 have infinitely many solution

Answer 1

Answer: Yes

Step-by-step-explanation: First distribute the 4 through the parentheses to get 20x + 12.

So the problem now reads 20x + 12 - 9x = 11x + 12.

Before adding or subtracting anything from both sides of the equation, make sure you simplify the left side as much as possible. 20x - 9x is 11x.

So the left side simplifies to 11x + 12 = 11x + 12.

Notice that when you try to put your variables together on one side of the equation by subtracting 11x from both sides, the x terms cancel out on both sides and we no longer have a variable in the equation.

Notice however that we're left with the statement 12 = 12. Since 12 = 12 is a true statement, we say that the solution to this equation is all real numbers which means the equation happens to have an infinite number of solutions

So, this equation would have infinitely many solutions.  

Answer 2

Answer:

YES

Step-by-step explanation:

$4(5x+3)-9x=11x+12\qquad\text{use the distributive property}\\\\(4)(5x)+(4)(3)-9x=11x+12\\\\20x+12-9x=11x+12\qquad\text{combine like terms}\\\\(20x-9x)+12=11x+12\\\\11x+12=11x+12\qquad\text{subtract}\ 11x\ \text{from both sides}\\\\11x-11x+12=11x-11x+12\\\\12=12\qquad\bold{TRUE}$

We received a true equation independent of x.

Hence, we conclude that we can substitute any number for x.

Therefore, the equation has infinitely many solutions (each number is the solution to this equation).