Can someone show me how they would solve this math equation?

Question

(5x-1) / 2 + (x-3) / 7 = 2x - 1/3

note: the slash marks represent the fraction line. I know what the answer is but i did it a really long way, i had to use a common denomonator (which was 42). Anyway, the answer i got was x = 25 / 27 I was just wondering if first, i did it right, and is there an easier way of finding out the answer?

Thanks for all your responses! I just found the LCD and simplifyed until the only thing left to do was cross multiply. After that i just solved the equation that i got. So im assuming the second response was wrong?

Answer 1

(5x-1) / 2 + (x - 3) / 7 = 2x - 1/3 = (6x - 3) / 3

7(5x - 1) + 2(x - 3) / 14 = (6x - 3) / 3

21 (5x - 1) + 6(x -3) = 14(6x - 3)

105x - 21 + 6x - 18 = 84x - 42

111x - 84x = 39 - 42

17x = -3

x = -3/17

So, kindly recheck your answer.

Answer 2

This is a classic struggle for Algebra 1 students, just because there is no SHORT way, only the easiest way.

The easiest way (for most people) is to look at every fraction in the equation and find the LCD. Your denominators (going across) are 2, 7, 1 (since you have 2x/1), and 3. The LCD of 2, 7, 1, and 3 is 42.

So, now I multiply the entire equation by 42. Notice how the denominator cancels in every single fraction:

42 [ (5x - 1) / 2 + (x - 3) / 7 ] = 42 [ 2x - 1/3 ]

Gives me....

21(5x - 1) + 6(x - 3) = 84x - 14

Now, I just solve it like any equation, first getting rid of parentheses...

105x - 21 + 6x - 18 = 84x - 14

Then combining like terms...

111x - 39 = 84x - 14

Then adding and subtracting from both sides...

27x = 25

And, finally, solving for x:

x = 25/27.

So, yes, that's the right answer. Did you do it the same way?

Answer 3

what would i do fist is get rid of 3 in the domination to make it easier to solve.

multiply 3 for both sides
3 ((5x-1) / 2 + (x-3) / 7) = 3(2x - 1/3)

(15x - 3)/2 + (3x - 9)/7 = 6x - 1

Look for LCD, which is 14
7(15x - 3) / 14 + 2(3x - 9)/14 = 6x - 1

(105x - 21)/14 + (6x - 18)/14 = 6x - 1

(105x - 21 + 6x - 18) / 14 = 6x - 1

combine like terms and multiply 14 for both sides
111x - 39 = 84x - 14

subtract 84x for both sides
27x - 39 = -14

add 39 for both sdes
27x = 25

divide 27 for both sides
x = 25/27

Answer 4

First, I would multiply each term by 42. That would get rid of the 2, 3 and 7 in the denominators. Then multiply to remove the parenthesis, collect terms, and get:

x = /

Answer 5

No, there is no easier way