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1/5x+3/10x-3/20x=18-15

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2 Answers

Hello Randy,
 
The exercise appears to be interested in applying your skills finding and using the greatest common denominator, as well as some other basic features of algebraic equations.  You'll need to identify the factors of each denominator and, using appropriate representations of one like 2/2 or 4/4, multiply respective terms in order to obtain equal denominators.
 
Using another example:
 
(1/7)x + (3/21)x - (3/63)x = 4
 
The denominators in question are:
 
7, 21 (=3*7), and 63 (=3*3*7)
 
The first term, 7, requires the additional factors 3*3 in the denominator, and the second term, 21, requires an additional factor of 3 in the denominator, so because 1*a = a we may multiply each by the appropriate representation of one:
 
(9/9)*(1/7)x + (3/3)*(1/21)x - 3/63x = 4
 
(9/63)x + (3/63)x - (3/63)x = 4
 
Now that each terms' denominator is equal, we may add the terms on the left hand side of the equation:
 
(9/63)x = 4
 
And simplifying the fraction 9/63 by removing factors common to the numerator and denominator, 9 in this case:
 
(9/9)*(1/7)*x = 4
 
1*(1/7)*x = 4
 
(1/7)*x = 4
 
Then solving for x, by multiplying both sides of the equation by 7/1:
 
x = 28
 
That does it for that example Randy.  Does that make sense for you or did I misunderstand something?
 
48 isn't a valid answer because 1/5 * (48) + 3/10 * (48) - 3/20 * (48) calculates to a number much larger than 3.
 
You can start by combining like terms.  1/5 * x = 4/20 * x  and 3/10 * x = 6/20 * x.  You can now combine all the fractions on the left side of the equation.
 
(4 + 6 - 3)/20 * x = 18 - 15
 
7/20 * x = 3
 
(20/7) * 7/20 * x = 3 * 20/7
 
x = 3 * 20/7 = 60/7