Is not to take the equation out the ( ) ?

Question

64. A common mistake when solving equations is the following:
The equation: 2(x - 2) = x + 3
First step in solving: 2x -2 = x +3
Write a clear explanation of what error has been made. What could be done to
avoid this error?

Answer 1

You didn't distribute the two fully in the right side of the equation. The correct answer would be:

2(x - 2) = x + 3
2x - 4 = x + 3

Answer 2

One of two basic errors that occur often (that's why they are "basic"!) has occurred.

Either the person solving simply carelessly dropped the parentheses resulting in the "2x - 2" being used, or the person failed to take care in multiplying the contents of the parentheses by the "2."

The first error is usually seen when a person does the individual steps, but likes to rush through them and combine individual steps into one written step. For instance, one can divide both sides of an equation by 75 like this: 75x = 225, 75x/75 = 225/75, x = 3 OR could just write: 75x = 225, x = 3. The second way opens the door to a variety of errors including dropping parentheses because they take a moment to write and "I'll remember they go there" and thinking ahead to the next step and writing that next step's result for the one you are currently writing out and blowing on past it into the next step but using that wrong interim value for the input to the next step. To build on the last example, perhaps the x = 3 is the input to a next step of substituting for x in an "x + y" type simultaneous equation. Perhaps x + y = 10 so after substitution, you find y = 7. But you're thinking ahead while writing out the quick version, above, of dividing each side by 75 and end up writing x = 7 instead of x = 3 and without any critical thought (Why not? You worked it through already! You're just writing this guff to make the teacher happy, right?) one uses the x = 7 while writing out the last step and come up with y = 3. Got to dot the "i's" and cross the "t's" — NOT the other way around.

The second error is most usually seen in carefully crafted problems like this one. Note that the second part of the value in the parentheses ("2") is the same as the result of the multiplication of 2 * x, which will be performed first. The crafter of the problem seeks to separate wheat from chaff by giving you the opportunity for careless error if you are speeding through the problem faster than you are able to do so safely. You do the first multiplication and are looking forward in the problem while mechanically (carelessly) cranking out the rest of the parentheses' resolution and just write the "2" again because it feels right due to the 2x and you aren't really thinking about it anymore. And that's the end of getting the right answer.

Both errors are due to carelessness and plowing ahead with your brain when that's not really your forte. One must learn how much attention to focus on the steps and give at least that much focus. To be honest, you are almost NEVER in a time situation when you have pen and paper available that will not allow you to write it ALL out and do so paying attention to the step you are writing. It's just that it's boring. As simple as that. The nimble mind wants to leap ahead but does so without the minimum discipline required. This, more than the simple math involved is the true lesson that will help you daily in the rest of your life.

For instance, it will serve you in good stead when your wife/husband is droning on about something tedious and says something double-edged like "Do these pants make my butt look fat?" (alright, that's several edged and loaded with sharp points) and you field it nicely because you learned to pay enough attention to the moment in 7th grade math.

Answer 3

The mistake is in the labled first step it should read
: 2x -4 = x +3"

Answer 4

A distribution error was made. The person did not distribute the 2 throughout the ().

Answer 5

the error that had been made is that 2 was not properly distrubued over (x-2)
distributive property is a(b-c)=ab-ac therefore 2(x-2)=2x-2*2
which equals 2x-4=x+3

Answer 6

you also have to multiply -2 by 2 on the left side
2(x-2)=x+3
2x-4=x+3

Bonus:
x=7

Answer 7

2(x - 2) = x + 3
2x - 4 = x + 3.......everything inside bracket is X by 2

Answer 8

You have to multiply each summand by two so it should read
2x-4 =x+3