Carlos solved the equation below for x. His solution is x = 5. What mistake did Carlos make and how could he have verified his solution to know for certain that his answer is correct?
2x - 9 = 19
2x = 10
x = 5
What mistake did Carlos make explain in detail and answer like a 12 year old girl
Carlos made a mistake when he divided both sides of the equation by 2 to solve for x. He should have divided both sides by 2 instead of just dividing the right side by 2.
To verify his solution, Carlos could have substituted the value of x (which is 5) back into the original equation and checked if both sides are equal. So, he could have replaced x with 5 in the equation 2x - 9 = 19. If he got a true statement like 2(5) - 9 = 19, then he would know for certain that his answer is correct.
What could carlos have done to check his answer
To check his answer, Carlos could have substituted the value of x (which is 5) back into the original equation and checked if both sides are equal. So, he could have replaced x with 5 in the equation 2x - 9 = 19. By calculating 2(5) - 9, Carlos could verify if the left side of the equation is equal to the right side of the equation (19). If he got the same number on both sides, it would mean that his solution is correct.
Hey there! So, it looks like Carlos made a tiny mistake. When he solved the equation 2x - 9 = 19, he correctly added 9 to both sides of the equation to isolate the term with x. But then, he divided both sides by 2 to solve for x, which is where he made the mistake.
See, when Carlos divided both sides by 2, he forgot to divide the 9 by 2 as well. So, instead of just dividing the 19 by 2, he should have divided 9 by 2 too. Let me show you how to do it correctly:
2x - 9 = 19
First, add 9 to both sides to isolate 2x:
2x - 9 + 9 = 19 + 9
This simplifies to:
2x = 28
Now, to solve for x, we need to divide both sides by 2. So, let's do that:
2x / 2 = 28 / 2
The 2's on the left side cancel out, and we get:
x = 14
So, the correct solution is x = 14, not 5. Now, how could Carlos have verified his solution to know for certain that his answer is correct? Well, he could have substituted his solution 5 back into the original equation and checked if it holds true. If it does, then he would know that his answer is correct.