Carlos solved the equation below for x. His solution is x=5. What mistake did Carlos make and how could have verified his solution to know for certain that his answer is correct?
2x-9=19
2x=10
x=5
The mistake Carlos made was when he divided both sides of the equation by 2. The correct equation would be 2x - 9 = 19, and when solving for x correctly, we would have:
2x - 9 = 19
Adding 9 to both sides: 2x = 28
Dividing both sides by 2: x = 14
To verify his solution, Carlos could have substituted the value of x back into the original equation and checked if it holds true. For example:
2(5) - 9 = 19
10 - 9 = 19
1 = 19
Since the equation does not hold true, Carlos would realize that his solution is incorrect.
What mistake did Carlos make? Explain in detail.
Apologies for the incorrect explanation in my previous response. Upon reviewing the given equation and solution, it seems there was no mistake made by Carlos.
The given equation is: 2x - 9 = 19.
Carlos correctly isolated x on one side of the equation by adding 9 to both sides:
2x - 9 + 9 = 19 + 9
2x = 28
Next, he divided both sides by 2 to solve for x:
(2x)/2 = 28/2
x = 14
So, Carlos's solution x = 5 is incorrect. My previous response was incorrect in stating that he made a mistake when dividing both sides of the equation by 2. Carlos's mistake was actually in his original solution stating that x = 5, which does not satisfy the equation 2x - 9 = 19.
To verify the correct solution, Carlos could have substituted x = 14 back into the original equation:
2(14) - 9 = 19
28 - 9 = 19
19 = 19
Since the equation holds true, Carlos would have known for certain that his answer x = 14 is the correct solution.
What could Carlos could have done to check his answer?
To check his answer, Carlos could have substituted the value of x = 5 back into the original equation and observed if it holds true.
The original equation is: 2x - 9 = 19.
Substituting x = 5:
2(5) - 9 = 19
10 - 9 = 19
1 = 19
Since 1 is not equal to 19, we can conclude that Carlos's solution of x = 5 is incorrect.
To avoid this mistake, Carlos could have checked his solution by substituting the value of x = 5 back into the equation and verifying that both sides of the equation are equal:
2(5) - 9 = 19
10 - 9 ≠ 19
By observing that the equation is not balanced when x = 5, Carlos would have known for certain that his answer is incorrect.
What is the correct answer? (By the way all of your explanations are correct)
I apologize for the inconsistent and confusing responses. Upon double-checking the equation, the correct solution is indeed x = 14.
Given equation: 2x - 9 = 19
To solve for x:
2x - 9 + 9 = 19 + 9
2x = 28
Divide both sides by 2:
(2x)/2 = 28/2
x = 14
Therefore, the correct solution to the equation 2x - 9 = 19 is x = 14.
No, it's fine, all your answers are correct. What is the correct answer? Show all steps in inverse operations to solve for x
Apologies for any confusion caused. Let's go through the steps to solve the equation and find the correct answer for x.
Given equation: 2x - 9 = 19
To solve for x, we will perform inverse operations to isolate the variable x.
Step 1: Add 9 to both sides to isolate the 2x term.
2x - 9 + 9 = 19 + 9
2x = 28
Step 2: Divide both sides by 2 to solve for x.
(2x)/2 = 28/2
x = 14
Therefore, the correct answer is x = 14.
Carlos made a mistake when he divided both sides of the equation by 2 in the second step. Let's break it down:
The original equation is:
2x - 9 = 19
To solve for x, Carlos correctly isolated the variable on one side by adding 9 to both sides to get:
2x = 28
Now, here's where Carlos made a mistake. Instead of dividing both sides of the equation by 2, he divided by 2 on one side only, resulting in:
x = 5
To verify the solution and determine if it is correct, Carlos could have substituted the value of x back into the original equation and checked if both sides are equal:
Substituting x = 5 into the original equation:
2(5) - 9 = 19
10 - 9 = 19
1 = 19
Since 1 is not equal to 19, Carlos would have realized that his answer, x = 5, is incorrect. He should have identified his mistake when he obtained a false statement by substituting the solution back into the original equation.