4 ( x + 40) = x , 100 - x = x.

Question

Word Problems - Finding the Variables.  I am able to convert the word problems,

but I'm finding it difficult to take the next step to find the answers for x.

Answer 1

4 (x+40) = x    100-x =x

take the first equation 4(x+40)=x and multiply out the 4

4x + 160= x,      100-x =x

now for the first equation, 4x + 160 = x   subtract 4x from both sides

160 = -3x   finally divide each side by a -3

160/-3 =  -3x/-3

160/-3 or -53.333 = x ( for the first equation)

for the second equation, 100 - x = x add x to both sides

100 = 2x divide each side by 2

x = 50 ( for the second equation)

Answer 2

Hello Al or Math Helper,

Thank you for the math answer.  I worked through your steps and have a few questions:

How and what helped you to determine dividing both sides by -3 was needed?  Is there

a fraction rule? What not use 4, 5, or 6 to complete the equation? Please explain.

Thanks

Comments

Hi, i'm not Al but i thought i'd try to help explain. You're right that any equation can be divided, multiplied or whatever, by any number that you want as long as you do the same thing to both sides of the equation. However, in this case you want to find the value of 'x', i.e. 'x' on it's own, not 'x' multiplied by -3, so you simply divide both sides of the equation by -3 to find the value of 'x'.

For example, say you had equation: 6x = 24
If you now wanted to find the value of 'x' you would divide both sides of the equation by 6. So you would get:
6x/6 = 24/6
So x = 4

Hope that helped, and feel free to ask more if you still have questions.  :)