sarah and jose were trying to solve the problem below. which one was incorrect and why? (it shows their responses step-by-step)
there is an image of two parallel lines and a transversal, both angles are same side interior, one angle is (5x+3) degrees and the other angle is (9x+33) degrees, both of these angles are supplementary
jose's answer:
5x+3+9x-33=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 was incorrect.
In Sarah's step, she made an error in subtracting 33 from both sides of the equation. It should have been:
5x + 3 = 9x - 33
36 = 4x
But then she divided 36 by 4 to solve for x, which is incorrect. The correct step would be to divide both sides of the equation by 4:
36/4 = 4x/4
9 = x
Jose's answer is incorrect because he made a mistake when combining like terms.
Step 1: Jose correctly set up the equation as 5x+3+9x-33=180.
Step 2: He combined like terms on the left side by adding 5x and 9x, which gave him 14x.
Step 3: However, he made a mistake when combining the constants on the left side. Instead of subtracting 33 from 3, he incorrectly subtracted 33 from 9x.
The correct equation should be: 14x-30=180.
From here, Jose made another mistake by dividing both sides of the equation by 14. Since 14x-30 does not evenly divide into 180, the solution he obtained, x=15, is incorrect.
On the other hand, Sarah's answer is correct. She correctly set up the equation as 5x+3=9x-33. By subtracting 4x from both sides, she obtained the correct solution x=9.
To determine which one of Sarah and Jose is incorrect, let's solve the problem step-by-step.
The problem states that the two angles are supplementary, meaning their sum is 180 degrees. Let's set up an equation to represent this:
5x + 3 + 9x + 33 = 180
Now let's solve it using Jose's approach:
Step 1: Combine like terms:
14x + 36 = 180
Step 2: Subtract 36 from both sides:
14x = 144
Step 3: Divide both sides by 14:
x = 144/14
Simplifying further,
x ≈ 10.29
Therefore, according to Jose's approach, x is approximately 10.29.
Now let's look at Sarah's approach:
Step 1: Set up the equation:
5x + 3 = 9x - 33
Step 2: Add 33 to both sides:
5x + 36 = 9x
Step 3: Subtract 5x from both sides:
36 = 4x
Step 4: Divide both sides by 4:
x = 36/4
Simplifying further,
x = 9
According to Sarah's approach, x is 9.
Comparing the values of x from both approaches, we can see that Jose obtained x ≈ 10.29, while Sarah obtained x = 9.
Therefore, Sarah's answer is incorrect, as she made an error in solving the equation.