x/2 - 4/5 +x/5 +3x/10=1/4 solve please
Answers
Answer:
x = 21/20
Step-by-step explanation:
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How can I solve x/5+1/4=x/2?
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To solve the given equation with fractions that have different denominators, 2, 4, and 5, you have to first determine the lowest common denominator for all three fractions, that is, the least common multiple (LCM) of all three denominators: 2, 4, and 5, i.e., the smallest number that all 3 denominators will divide into evenly. The least common multiple of all three denominators turns out to be 20.
The next step is to clear the given equation, x/5 + 1/4 = x/2, of fractions by multiplying both sides of the equation by the LCM, 20, as follows:
x/5 + 1/4 = x/2 (Given)
20(x/5 + 1/4) = 20(x/2)
20(x/5) + 20(1/4) = 20(x/2)
(20/5)x +20/4 = (20/2)x
4x + 5 = 10x
The next step is to isolate x on one side of the equation as follows:
Subtract 4x from both sides:
4x - 4x + 5 = 10x - 4x
0 + 5 = 6x
5 = 6x
Now that x is isolated on the right side, divide both sides by 6 to finally solve for x:
5/6 = (6x)/6
5/6 = (6/6)x
5/6 = (1)x
5/6 = x
CHECK:
x/5 + 1/4 = x/2
(5/6)/5 + 1/4 = (5/6)/2
(5/6)(1/5) + 1/4 = (5/6)(1/2)
1/6 + 1/4 = 5/12
Since the LCM of 4, 6, and 12 is 12, then we can convert each fraction to an equivalent one with 12 as the denominator:
(1/6)(1) + (1/4)(1) = 5/12
(1/6)(2/2) + (1/4)(3/3) = 5/12
2/12 + 3/12 = 5/12
5/12 = 5/12
Therefore, x = 5/6 is indeed the solution to the given equation.