Solve 6x=3a+12?

Question

Is the above written correctly based on the word problem?

6 times a number equal 3 times a number plus 12

Is the above written correctly based on the word problem....6 times a number equal 3 times a number plus 12

I thought it was 6x=3x+12 but I was told I was wrong

Answer 1

Solving is impossible as it is a single linear equation in two variables, but I will express one variable in terms of the other:

6x = 3a + 12
2x = a + 4 (Dividing by 3 throughout)
x = (a + 4)/2 ..... (1)

6x = 3a + 12
2x = a + 4
a = 2x - 4 ..... (2)


In (1), if you put in a value of a, you get the corresponding values of x. There are infinite values. Here a is the independent variable and x is the dependent variable as the value of x depends on what the value of a is.

In (2), if you put in a value of x, you get the corresponding values of a. There are again infinite possible values. Here x is the independent variable and a is the dependent variable.

Here a few solution sets:
x = 4, a = 4
x = 1, a = -2
x = 3, a = 2
x = 0, a = -4
x = 2, a = 0

EDIT:
Hey guys, it says:
6 times A NUMBER = 3 times A NUMBER plus 12

Both are 'a number'. Anyone well-versed in grammar would know that the numbers multiplied with 6 and 3 are different. You must take same variable only if it says:
6 times a number = 3 times THE number plus 12

There's no THE.
You were not misled, Mimi
Your teacher was right. You cannot use the same variable.

Answer 2

If it's 6x=3a+12 then
x=1/2a+2
then you can pick any value for a and easily find x
if a=2 then x=1/2*3+2=1+2=3 etc.

if it's 6x=3x+12 then
6x=3x+12 | -3x
3x=12 |:3
x=4

Answer 3

Hi,

No, keep everything in one variable. If it says "6 times A NUMBER. and then that's equal to 3 times THE SAME NUMBER, . . ." then use the same variable. The equation you should be working with should look like the following:

6x = 3x + 12

Subtract 3x from both sides of the equation . . .

3x = 12

Divide both sides of the equation by 3 . . .

x = 4 <==== FINAL ANSWER

I hope that helps you out! Please let me know if you have any other questions!

Sincerely,

Andrew

Answer 4

No, you're making this more difficult than necessary.

If your word problem is this: 6 times a number equal 3 times a number plus 12

Then you would write it like this: 6x = 3x + 12. BECAUSE: It's saying 3 times a number, not 3 times A.

Therefore, your answer would be (including work):

6x = 3x + 12
6x - 3x = 12
3x = 12
x = 12/3
x = 4

Best Wishes.

Answer 5

x=4,a=4

Answer 6

what is a? If it is a constant then
x=(3a+12)/6
=(a+4)/2

If a is a variable then you need another equation of x & a to solve this.