Debbie finished her algebra test early so she decided to check each of her answers. After checking her answer to question #10, she realized she made a mistake in her solution. In which step does Debbie make her mistake?
Original Equation: 2 + 3y = 5(y - 2)
Step One: 2 + 3y = 5y - 10
Step Two: 2 = 2y - 10
Step Three: -8 = 2y
Step Four: -4 = y �¨ y = -4
1
2
3
4
Step 2: because instead of adding the like terms he subtracted them
Step 1 & 2 are right. She made the first mistake in Step 3, it should be
2 + 10 = 2y
12 = 2y
And so the succeeding steps are wrong too. But the earliest was in step 3.
hope this helps :3
To find the step in which Debbie made a mistake, we need to compare each step of her solution with the original equation and look for any inconsistencies. Let's go through each step and see if there are any errors.
Original Equation: 2 + 3y = 5(y - 2)
Step One: 2 + 3y = 5y - 10
In this step, Debbie distributed the 5 to both terms inside the parentheses. This is correct.
Step Two: 2 = 2y - 10
In this step, Debbie subtracted 3y from both sides to isolate the y term. This is also correct.
Step Three: -8 = 2y
In this step, Debbie combined like terms on the right side of the equation. However, there is a mistake in this step. To simplify 2y - 10, we need to subtract 10 from both sides, not just 2y.
The correct step three would be:
2 - 10 = 2y - 10
-8 = 2y - 10
Step Four: -4 = y/2
In this step, Debbie divided both sides by 2 to isolate y. However, there is another mistake in this step. When subtracting 10 in the previous step, we need to subtract 10 from both sides, not just 2y. Therefore, dividing both sides by 2 is incorrect.
The correct step four would be:
-8/2 = 2y/2
-4 = y
So, the mistake Debbie made in her solution is in Step Three.