Question

what is the solution of the equation 5/3-2x=1/6?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation 5/3 - 2x = 1/6, you can follow these steps:

1. Begin by subtracting 5/3 from both sides of the equation.
(5/3 - 2x) - 5/3 = 1/6 - 5/3

Simplifying the left side:
-2x = 1/6 - 5/3

2. Next, simplify the right side by finding a common denominator for the fractions.
-2x = 1/6 - 10/6

3. Combine the fractions on the right side.
-2x = -9/6

4. Simplify the right side of the equation.
-2x = -3/2

5. Divide both sides of the equation by -2 to solve for x.
(-2x)/-2 = (-3/2)/-2

Simplifying:
x = 3/4

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

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the equation 5/3 - 2x = 1/6, follow these steps:

Step 1: Get rid of the fractions by multiplying the entire equation by the least common multiple (LCM) of the denominators. In this case, the LCM of 3 and 6 is 6. So, multiply both sides of the equation by 6.

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

Simplifying this gives:

10 - 12x = 1

Step 2: Move all the variables to one side of the equation. In this case, move the -12x to the right side by adding 12x to both sides of the equation.

10 - 12x + 12x = 1 + 12x

Simplifying this gives:

10 = 1 + 12x

Step 3: Move all the constants to the other side of the equation. In this case, subtract 1 from both sides of the equation.

10 - 1 = 1 + 12x - 1

Simplifying this gives:

9 = 12x

Step 4: Solve for x by dividing both sides of the equation by 12.

9/12 = (12x)/12

Simplifying this gives:

3/4 = x

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

Answer 3

[AI-generated answer — Explain Bot]

To find the solution of the equation 5/3 - 2x = 1/6, we need to isolate the variable "x" on one side of the equation.

Step 1: Start by subtracting 5/3 from both sides of the equation:
(5/3 - 2x) - 5/3 = 1/6 - 5/3
(-2x) = 1/6 - 5/3

Simplifying the right side:
(-2x) = (1/6) - (5/3)

Step 2: Find a common denominator for the fractions on the right side of the equation. The common denominator for 6 and 3 is 6.
(-2x) = (1/6)*(1/1) - (5/3)*(2/2)
(-2x) = 1/6 - 10/6

Simplifying the right side:
(-2x) = (1 - 10) / 6
(-2x) = (-9) / 6

Step 3: Divide both sides of the equation by -2 to solve for x:
(-2x) / -2 = (-9) / 6
x = 9 / (-6)

Simplifying the right side:
x = -3/2

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