Question

the following equation was solved incorrectly for x2(x - 3) + 7 = 62x - 3 + 7 = 62x + 4 = 62x = 2x = 1explain what mistake the student made, correct it and finish the equation correctly. show all work

Answer 1

We want to solve the following equation

`2\cdot(x-3)+7=6`

First, we start by distributing the multiplication on the left side, so we have

`2x-6+7=6`

Note that if we compare this step to the second step of the given procedure, the mistake occured on the distribution of the multiplication. So, instead of writing -6, the mistake was to write -3.

Now, we continue to solve the equation from this point. First, we operate on the left side, so we get

`2x+1=6`

Now, we subtract 1 from both sides

`2x=6-1=5`

Then, we divide both sides by 2. So we get

`x=(5)/(2)`