Sarah and Jose were trying to solve the problem. Which one was INCORRECT and why? The image shows 2 parallel lines and an intersecting lines which create two angles (5x+3) and (9x-33).
Jose's Answer:
5x+3+9x-22=180
14x-30=180
14x=210
x=15
Sarah's answer:
5x+3=9x-33
3=4x-33
36=4x
x=9
Sarah's answer was incorrect.
In her equation, she subtracted 33 from both sides of the equation instead of adding it to both sides. The correct equation should be 5x + 3 = 9x + 33. So, her solution of x=9 is incorrect.
The incorrect answer is Sarah's answer: 5x+3=9x-33.
To solve for x in this equation, we need to isolate the variable on one side of the equation. Let's go through the steps:
1. Start with the equation: 5x+3=9x-33.
2. Begin by moving the variable term (9x) to one side of the equation and the constant term (-33) to the other side. To do this, we can subtract 5x from both sides:
5x - 5x + 3 = 9x - 5x - 33,
3 = 4x - 33.
At this point, Jose's answer (5x+3+9x-22=180) is still correct.
3. Now, to get x on its own, we need to isolate the term (4x) on one side of the equation. Start by adding 33 to both sides:
3 + 33 = 4x - 33 + 33,
36 = 4x.
4. Finally, divide both sides by 4 to solve for x:
36/4 = (4x)/4,
9 = x.
So, the correct value of x is 9.
Therefore, Sarah made a mistake when she incorrectly calculated that x=9. The correct value of x is indeed 15, as Jose calculated.
To determine which one of them provided the incorrect answer, we need to compare their solutions step by step.
Let's start with Jose's answer:
Jose wrote down the equation 5x + 3 + 9x - 22 = 180. He then simplified the equation by combining like terms: 14x - 19 = 180.
However, there was an error in his equation. The -22 should have been combined with the +3 to be -19, not -22. Therefore, Jose's equation should have been 5x + 3 + 9x - 19 = 180.
Let's fix this error and continue evaluating his solution:
14x - 19 = 180
Adding 19 to both sides: 14x = 199
Finally, dividing both sides by 14 gives us x = 199/14, which is approximately 14.214.
Next, let's move on to Sarah's answer:
Sarah started with the equation 5x + 3 = 9x - 33. She then solved for x by isolating the variable:
Subtracting 5x from both sides: 3 = 4x - 33
Adding 33 to both sides: 36 = 4x
Finally, dividing both sides by 4 yields x = 36/4, which is 9.
Now that we have both solutions, we can see that Sarah's answer of x = 9 is indeed correct, while Jose's answer of x = 14.214 is incorrect due to the error in his equation.