Sehyr solved the equation w/2−7=11. She seems to have made an error in her work because the solution she found does not work. Observe Sehyr’s work to find her error and correct it to find the solution to the equation.
Sehyr’s work:
w/2−7=11
w/2−7+7=11+7 Using the Addition Property of Equality
w/2/2=18/2 Using the Division Property of Equality
w=9
The solution to the equation is
w = 9.
w=9
Sehyr's error is in the step when she added 7 to both sides of the equation. Instead of adding 7, she should have added 14 since she added 7 to both sides.
Correcting the mistake:
w/2 - 7 + 14 = 11 + 14
w/2 + 7 = 25
Now, to isolate w, we can multiply both sides of the equation by 2:
2(w/2 + 7) = 2(25)
w + 14 = 50
Finally, we can solve for w by subtracting 14 from both sides:
w = 50 - 14
w = 36
So, the correct solution to the equation is w = 36.
To find Sehyr's error, let's analyze her steps:
1. w/2 - 7 = 11
2. w/2 - 7 + 7 = 11 + 7 (Using the Addition Property of Equality)
3. w/2/2 = 18/2 (Using the Division Property of Equality)
4. w = 9
The error occurs in step 3. Sehyr divides both sides of the equation by 2, instead of dividing only the term w/2 by 2.
To correct it, we need to isolate the variable w. Let's rewrite the equation from step 1:
w/2 - 7 = 11
To eliminate the -7 term, we can add 7 to both sides:
w/2 - 7 + 7 = 11 + 7
w/2 = 18
Now, we need to isolate w/2 by multiplying both sides by 2:
(w/2) * 2 = 18 * 2
w = 36
Therefore, the correct solution to the equation is w = 36.