Question

1)Lin solved the equation incorrectly. Find all the errors in her solution. (Select all appropriate answers.)Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.Step 1 to Step 2: Lin distributed 8(x - 3) incorrectly; should be 8x - 3.Step 2 to Step 3: Lin calculated 8x - 24 + 7 incorrectly; should be 8x - 31.Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.What should Lin's answer have been ?8 ( x - 3 ) + 7 = 2x ( 4 - 17 )answer choices :x = 3/2 x = 1/2x = 1/5x = 1/3

Answer 1

Answer:

Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.

Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.

Lin's answer should be x = 1/2

Explanation:

The initial expression is:

8(x - 3) + 7 = 2x(4 - 17)

So, the first error is in step 1, because 4 - 17 = - 13, then step 1 should be:

8(x - 3) + 7 = 2x(-13)

Then, we can apply the distributive property as:

8x - 8(3) + 7 = -26x

8x - 24 + 7 = -26x

We need to add similar terms:

8x - 17 = - 26x

Then, we can subtract 8x from both sides as follows:

8x - 17 - 8x = - 26x - 8x

-17 = -34x

Finally, we can divide by -34 as follows:

-17/(-34) = -34x/(-34)

1/2 = x

Therefore, the answers are:

Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.

Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.

Lin's answer should be x = 1/2