A common mistake when solving equations is the following:?

Question

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

when removing bracket than we have to multiply that amount with each and every item of that group

here the error is you had multiply tht with X but not with 2

so the correct equation would be

2x-4=x+3

which the ans is x=7

cheers

Answer 2

The first step used in solving this equation is incorrect. In this case you have to use the distributive property to get the numbers out of the parentheses. The bracket must be expanded in order to correctly solve the equation.

ie.
2(x-2) = x+3
2(x)-2(2) = x+3
2x-4=x+3
2x-x=3+4
x=7

Answer 3

That's a break in the distributive property of multiplication.

A multiplicand must operate on all terms in a polynomial within a bracket. In the bracket are two terms, a binomial. The multiplicand will operate on both.

Students could expand the bracket before multiplying:

eg: [(2 * x) - (2 * 2)] = 2x - 4

The minus 2 makes that a touch confusing for some students.

Have the students count the number of terms in the bracket. They must multiply each on by 2. So I'd do 2 * something twice. The minus sign confuses some students - I tell mine that the minus sign is "owned" by the number directly after it, in this case 2. So the two operations are 2 * x and 2 * -2

Answer 4

The mistake is that 2(x-2) = 2x -4, not 2x -2. 2 was multiplied only by x, but not by 2.

Is this a common mistake?? I don't know. To avoid this, all you have to do is pay attention. Don't try to solve equations after drinking several cans of beer.

Answer 5

The equation became into: 2(x - 2) = x + 3 there became into an errors interior the 1st step in fixing. once you distribute a(b + c), it equals ab + ac, no longer ab + c . as a result, the incredible first step in fixing could be: 2x - 4 = x + 3 the 1st step in fixing would not be: 2x - 2 = x + 3 i'm hoping this helped!

Answer 6

the 2 must be multiplied by both quantities inside the parentheses. 2(x - 2) = 2x - 4


This is called the distributive property.

Then you can solve 2x - 4 = x + 3
x - 4 = 3
x = 7

Answer 7

It's an error of not properly distributing the 2.
What could be done to avoid such an error?
Be more careful, and be aware of the possibility of making such errors. Check over your final answer in the original equation.