1. 5/3-2x=1/6

Answer 1

To solve the equation 5/3 - 2x = 1/6, we will first simplify by finding the common denominator.

Recall that the common denominator of 3 and 6 is 6.

Multiplying the fraction 5/3 by 2/2 to obtain the same denominator:
(5/3) * (2/2) = 10/6

So now our equation becomes: 10/6 - 2x = 1/6

Next, we subtract 10/6 from both sides of the equation to isolate the term with x:
10/6 - 10/6 - 2x = 1/6 - 10/6

This simplifies to: -2x = -9/6

To eliminate the negative sign, we can multiply both sides of the equation by -1:
-1 * (-2x) = -1 * (-9/6)
This gives us: 2x = 9/6

Now, we will simplify the fraction on the right-hand side.
9/6 can be reduced by dividing the numerator and the denominator by their greatest common divisor, which is 3.
After dividing 9 by 3 and 6 by 3, we have 3/2.

So our equation now becomes: 2x = 3/2

To solve for x, we divide both sides of the equation by 2:
(2x)/2 = (3/2)/2

This gives us: x = 3/4

Therefore, the solution to the equation 5/3 - 2x = 1/6 is x = 3/4.