Question

I

6. Identify and correct the error in the following solution.
(nearest tenth)
-3.1(2n + 3) = 12.3
-6.2n + 3 = 12.3
-6.2n + 3 - 3 = 12.3 - 3
-6.2n = 9.3
-6.2n 9.3
-6.2 -6.2
n= -1.5

Answer 1

The error is in line 2 of the original solution. They did NOT multiply the constant inside the bracket by the constant outside the bracket.

Correct solution:

-3.1(2n + 3) = 12.3

Expand the brackets:

⇒ -3.1 · 2n - 3.1 · 3 = 12.3

⇒ -6.2n - 9.3 = 12.3

Add 9.3 to both sides:

⇒ -6.2n - 9.3 + 9.3 = 12.3 + 9.3

⇒ -6.2n = 21.6

Divide both sides by -6.2:

⇒
`(-6.2)/(-6.2n)=(21.6)/(-6.2)`

⇒
`n = -(108)/(31)`

⇒ n = -3.5 (nearest tenth)