Could you please check my work?
3/(x-7)=2/(2x+1)
3(2x+1)=2(x-7)
6x+3=2x+-14
x=-4.25
I appreciate it.
good work,
all steps are correct
To check your work, we need to substitute the value of x back into the original equation and see if it satisfies it. Let's do that.
Original equation:
3 / (x - 7) = 2 / (2x + 1)
Substituting x = -4.25:
3 / (-4.25 - 7) = 2 / (2(-4.25) + 1)
3 / (-11.25) = 2 / (-8.5 + 1)
3 / (-11.25) = 2 / (-7.5)
-0.2667 = -0.2667
Since both sides are equal, it means that the supplied value of x = -4.25 is indeed a valid solution to the equation. Your work is correct.
To check your work, we will substitute the value of x that you found, which is -4.25, back into the original equation and verify if both sides are equal.
Original equation: 3/(x - 7) = 2/(2x + 1)
Substituting x = -4.25:
Left-hand side: 3/((-4.25) - 7) = 3/(-11.25) = -0.2667 (rounded to four decimal places)
Right-hand side: 2/(2(-4.25) + 1) = 2/(-8.5 + 1) = 2/(-7.5) = -0.2667 (rounded to four decimal places)
Since both sides of the equation yield the same value of -0.2667, we can conclude that your solution, x = -4.25, is correct. Well done!