Solving $3x - 40 \cdot 2 = x + 5$

Question

What did I do wrong?

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Start problem
got rid of the 2 on the left side by reversing the multiplication
simplified - got rid of the two on the left side and divided on the right to get 2.5
undoing the subtraction of 40 by adding 40 to both sides
simplified - got rid of the 40 on the left side and added 40 to 2.5 on the right.
Undoing the multiplication of 3 on the left side by dividing by 3 on both sides.
Simplifying - got rid of the 3 on the left, and divided on the right
undid addition of x on right side by subtracting x on both sides
simplified ------ confusion

Sorry but try to improve your writing and especially the number 2 which is unreadable. — , Mar 19 '14 at 18:52
@Sami I can write better on paper, I did this digitally with a mouse. I thought it was good enough to where it was legible though. — user3402545, Mar 19 '14 at 18:54
considering that he commented every step it is completely readable to me. user3402545: Using TeX is still the usual way to write formulae in questions, consider using it in the next questions — Alessandro Codenotti, Mar 19 '14 at 19:01

score 5 · Accepted Answer · answered Mar 19 '14 at 18:56

5

Your mistake is in step 2. If you're going to divide either side of the equation by $2$, you have to divide the entire equation on both sides. You did: $$3x-\dfrac{40 \times 2}{2} = x+\dfrac{5}{2}$$ However, this is incorrect. The correct way to carry this out would be: $$\dfrac{3x - 40 \times 2}{2} = \dfrac{x+5}{2}$$ But that's not really the easiest way to solve this. Try subtracting $x$ from both sides first. That leaves us with: $$2x-40 \times 2=5$$ Try to take it from here.

answered Mar 19 '14 at 18:56

foobar1209

1,047

Quick question - Why would that leave us with 2x - 40 * 2 = 5? Why is it not 3x - 40 * 2 = 5? – user3402545 Mar 19 '14 at 19:03
@user3402545 Because if you want to subtract $x$ from one side of the equation, you have to subtract it from the other side as well so that the equality is maintained. – foobar1209 Mar 19 '14 at 19:07
Thanks for the help! I forget that x is really 1x -------- x = 42.5 – user3402545 Mar 19 '14 at 19:15

score 1 · Answer 2 · answered Mar 19 '14 at 18:55

You divided some but not all of each side of your equation in step 2.

The result of dividing by 2 in step 2 should be $(3x-40\cdot 2)/2 = (x+5)/2$ which is $(3/2)x-40 = x/2+5/2$ which is $1.5x-40=0.5x+2.5$.

The next mistake occurs in line 7 where you have $...=\frac{x+42.5}{3}$ and then on the next line you have $x+42.5/3$ where you should have $x/3+42.5/3$ (the 3 divides both $x$ and $42.5$).

score 1 · Answer 3 · answered Mar 19 '14 at 18:56

1

You didn't divide the x on the right by 2 and didn't treat the multiplication on the left appropriately

It should go more like this $3x - 40 \cdot 2 = 3x - 80 = x + 5$

$2x-80=5$

$2x = 85$

$x = \frac{85}{2}$

answered Mar 19 '14 at 18:56

ruler501

1,218

Solving $3x - 40 \cdot 2 = x + 5$

3 Answers3