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
9=x
Sarah's answer is incorrect.
In her equation, she mistakenly subtracted 33 from the left side of the equation instead of adding it. This error results in an incorrect value for x. The correct equation should be:
5x + 3 = 9x - 33
First, let's subtract 5x from both sides to isolate the variables:
3 = 4x - 33
Next, let's add 33 to both sides to isolate the variable term:
36 = 4x
Finally, divide both sides by 4 to solve for x:
x = 9
Sarah's answer was incorrect. Let's break down the steps to see why.
The problem states that the angles formed by the intersecting lines are (5x+3) and (9x-33).
Jose correctly set up an equation by stating that the sum of the angles is equal to 180 degrees:
(5x + 3) + (9x -33) = 180
Sarah's mistake was in setting up the equation. She equated the two angles directly:
5x + 3 = 9x - 33
By doing this, Sarah assumed that the sum of the angles is equal to one of the angles alone, which is incorrect.
Therefore, Sarah's answer is incorrect because she misinterpreted the problem and set up the equation incorrectly.
To determine which answer is incorrect and why, we need to check if the solution obtained from each equation satisfies the given problem.
First, let's evaluate Jose's solution. He started by setting up the equation:
5x + 3 + 9x - 22 = 180
Then, he combined like terms:
14x - 19 = 180
Next, move the constant term to the other side:
14x = 199
Finally, solve for x by dividing both sides by 14:
x = 199/14
Now, let's check if this value of x satisfies the given problem:
Angle 1: 5x + 3 = 5 * (199/14) + 3
Angle 2: 9x - 33 = 9 * (199/14) - 33
Evaluate each angle:
Angle 1: 5 * (199/14) + 3 ≈ 71.57 degrees
Angle 2: 9 * (199/14) - 33 ≈ 97.14 degrees
Since the sum of these angles is not equal to 180 degrees, Jose's solution is incorrect.
Now, let's evaluate Sarah's solution. She started by setting up the equation:
5x + 3 = 9x - 33
Next, she moved the x term to one side and the constant term to the other:
3 + 33 = 9x - 5x
Combine like terms:
36 = 4x
Finally, solve for x by dividing both sides by 4:
x = 36/4
x = 9
Now, let's check if this value of x satisfies the given problem:
Angle 1: 5x + 3 = 5 * 9 + 3 = 48 degrees
Angle 2: 9x - 33 = 9 * 9 - 33 = 18 degrees
The sum of these angles is 48 + 18 = 66 degrees, which is not equal to 180 degrees. Therefore, Sarah's solution is also incorrect.
Both Jose's and Sarah's solutions are incorrect because neither value of x satisfies the given problem.