If 1/3 + 1/2 + 1/x = 4, then x = A. 5/18 B. 6/19 C. 24/11 D. 19/6 E. 18/5
(B) To solve this equation, we first need to find a common denominator to simplify the equation. The lowest common denominator is 3 × 2 × x = 6x. If we multiply the both sides of the equation by 6x, we can get rid of all of the fractions.
Multiplying 1/3 + 1/2 + 1/x = 4 by 6x, we get: 6x/3 + 6x/2 + 6x/x = 4(6x).
Reducing this, we get: 2x + 3x + 6 = 24x 5x + 6 = 24x 6 = 19x, or x = 6/19.
Now you might be tempted to stop there, but if you have extra time you can double check by backsolving in for x. You can plug in 6/19 for x. 1/(6/19) is the same as 19/6. 1/2 = 3/6 and 1/3 = 2/6 so you can put everything in terms of 6ths and get: 2/6 + 3/6 + 19/6 = 24/6 = 4.
So, you can see with 100% certainty that the answer of 6/19 is correct.
The correct answer is choice (B). ---------- Hi. I didn't understand why we have to multiply both sides of the equation. What I did is finding LCD that is 6, and I did not multiply 4 by 6...
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