Post your 50-word response to the following:
Explain why the equation -6(x + 3) = -6x + 5 has no solution and 7x +18 + 8x = 8(x + 4) + 7x – 14 has infinitely many solutions.
-6x-18=-6x+5 0x=23 and can not have zero in the denominator. Division by zero is undefined.
15x+18=15x+18 0x=0 Well, if you take anything times zero the resulting product is zero.
How do I explain this in 50 words I don't even know how the answer was done?
Sure! I'll start by explaining why the equation -6(x + 3) = -6x + 5 has no solution. To solve this equation, you can simplify it by distributing -6 across the terms inside the parentheses:
-6 * x + (-6) * 3 = -6x + 5
-6x - 18 = -6x + 5
You can see that the variable "x" cancels out on both sides of the equation, resulting in a contradiction (-18 ≠ 5). Therefore, the equation has no solution.
Now, let's move on to the equation 7x + 18 + 8x = 8(x + 4) + 7x - 14. To solve this equation, you can start by simplifying both sides:
7x + 18 + 8x = 8x + 32 + 7x - 14
15x + 18 = 15x + 18
Here, you can see that the variable "x" cancels out on both sides of the equation, resulting in an identity (18 = 18). Since the equation is always true regardless of the value of "x," it has infinitely many solutions.
In summary, the first equation has no solution because it leads to a contradiction, while the second equation has infinitely many solutions because it simplifies to an identity.