solve the equation m, and check the solution: 5/6x-1/5x+4=7/10x
5/6x-1/5x+4=7/10x
25/30x - 6/30x + 4 = 21/30x
4 = 21/30x - 19/30x
4 = 2/30x
4/(2/30) = x
4 * (30/2) = x
120/2 = x
60 = x
Substitute 60 for x to see if my solution is correct.
Thanks for the help :)
You're welcome.
9x_43=_30x-4
To solve the equation, we need to isolate the variable x on one side of the equation. Let's go through the steps:
1. Start by simplifying both sides of the equation. We have:
(5/6)x - (1/5)x + 4 = (7/10)x
2. To combine the x terms on the left side, we need a common denominator for 5/6 and 1/5. The least common denominator (LCD) is 30. So, we multiply both terms by their respective denominators:
5/6 * (30/30)x - 1/5 * (6/6)x + 4 = (7/10)x
(25/30)x - (6/30)x + 4 = (7/10)x
3. Now, combine the x terms on the left side:
[(25/30)x - (6/30)x] + 4 = (7/10)x
(19/30)x + 4 = (7/10)x
4. To isolate the x term, we want to eliminate the fraction on the left side. We can multiply every term by the denominator of the fraction, which is 30:
30 * [(19/30)x + 4] = 30 * (7/10)x
19x + 120 = 21x
5. Next, move all the x terms to one side and the constant terms to the other side:
19x - 21x = -120
-2x = -120
6. Divide both sides of the equation by -2 to solve for x:
x = (-120) / (-2)
x = 60
To check the solution, substitute x = 60 back into the original equation and see if both sides are equal:
(5/6)(60) - (1/5)(60) + 4 = (7/10)(60)
50 - 12 + 4 = 42
Both sides of the equation equal 42, confirming that x = 60 is the correct solution.