Question 405101: Three times the sum of a number and six is equal to twice the number. Find the number.
Answer by IWork4Dessert(60)   (Show Source):
You can put this solution on YOUR website! Let this number be "x".
Break the problem apart. You know that three times the sum of a number(x) and 6 equals twice the number(x).
Start by taking all of the problem before the equal sign and putting into numbers.
Three times the sum of a number(x) and 6: 3(x+6)
Make sure to read the whole problem before you jump to conclusions about how to arrange the numbers, or you might write something like 3x+6.
You know what half of your equation looks like now.
3(x+6)=?
Now look back at the second half of the problem, where it says "...equals twice the number." You know that this part of the equation comes after the equal sign and that the number is x, so the second half of the equation must be 2x.
Now put this on the other side of the equation, after the equal sign.
3(x+6)=2x
Solve by distributing the three throughout the parentheses.
3x+18=2x
Subtract the 3x from the left side of the equation from the 2x on the right side of the equation.
3x+18=2x
-3x -3x
Which turns into:
18=-x
You can't finish off a problem with a negative variable, though, so you'll need to divide both sides by -1 to cancel it out.
x=-18
And there's your answer. You want to get the variable onto the other side of the equation with no numbers before or after it.
You can also check your answer by plugging it back into the equation:
3(-18+6)=2(-18)
-54+18=-36
-36=-36
Hope this helps :)
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