solve the equation . state the solution set and check yout answer when appropriate

0.12(a + 2) / 3 = 0.114

Question

solve the equation . state the solution set and check yout answer when appropriate

0.12(a + 2) / 3 = 0.114

anonymous · Answer

how do you solve it out?

mathmale · Answer

while not strictly necessary, multiplying both sides of this equation by 1000 will eliminate the (decimal) fractions.
Next, I'd suggest you multiply both sides of the resulting equation by 3, to remove that denominator of 3.
Would you please do these two things now.  Type out your answers.

anonymous · Answer

120 (a + 2) / 3 = 114   then   360 (a + 2) =342 @mathmale

mathmale · Answer

120 (a + 2) / 3 = 114  is fine.  Multiply both sides by 3, noting that the 3 in the numerator on the left side will cancel the 3 in the denominator on the left.  360 is not correct.  (Why?)

anonymous · Answer

oh I multiplied the 120 by the instead of canceling it out

anonymous · Answer

@mathmale

mathmale · Answer

Yes.  So, what is the correct result after you've multiplied both sides of the equation by 3?

anonymous · Answer

120 (a + 2) = 342 @mathmale

anonymous · Answer

@mathmale

mathmale · Answer

Looks good.  So much simpler without those fractions!  since this is an equation, you can proceed to solve it for the value of 'a'.  Know how to do that?
First, you might want to simplify this equation by finding the largest common factor of 120 and 342 and dividing both by that LCF.

mathmale · Answer

Hint:  is 3 a factor of both 120 and 342?  Is 3 the GCF (greatest common factor)?

anonymous · Answer

i did it and i got a=220

mathmale · Answer

You could now check your answer (a=220) by substituting it back into the original equation.  Does doing this make the original equation true?  if so, you know a=220 is the solution.

anonymous · Answer

i checked it and got 8.88 did i do something wrong

mathmale · Answer

$$0.12(a + 2) / 3 = 0.114$$Multiply both sides by 100 to obtain$$120(a+2)/3=114$$

mathmale · Answer

Next, $$120(a+2)=342$$

mathmale · Answer

Since we're looking to find the value of 'a,' please just divide both sides of this equation by 120.  What do you obtain by doing that?

anonymous · Answer

2.85?

mathmale · Answer

If you do that, you end up with a+2=2.85, right?
Try subtracting 2 from both sides of this equation.
What do you get?

anonymous · Answer

a=.85

anonymous · Answer

thank you

mathmale · Answer

Nice work.  Hope to work with you again soon!