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

$x=\frac{5}{2}$