Question

What is the solution of the equation 5 over 3 − 2(x)=1 over 6 ?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation, we need to isolate the variable x.

First, let's simplify the equation by multiplying both sides by 6 to get rid of the denominators:

6 * (5/3) - 6 * (2x) = 6 * (1/6)
(5/3) - 12x = 1

Next, let's get rid of the fraction by multiplying both sides by 3:

3 * (5/3) - 3 * (12x) = 3 * 1
5 - 36x = 3

Now, let's isolate the variable by moving constants to the other side:

-36x = 3 - 5
-36x = -2

Finally, divide by -36 on both sides to solve for x:

x = -2 / -36
x = 1/18

Therefore, the solution to the equation is x = 1/18.

Answer 2

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

To find the solution of the equation 5/3 - 2(x) = 1/6, we need to solve for the variable x.

Step 1: Simplify the equation.

Let's start by simplifying both sides of the equation separately.

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

Step 2: Distribute the 2 to the term inside the parentheses.

5/3 - 2x = 1/6

Step 3: Convert the fractions to a common denominator.

The common denominator of 3 and 6 is 6. So, we need to rewrite both fractions with a denominator of 6.

(5/3) * (2/2) = 10/6
(1/6) * (1/1) = 1/6

Now, the equation becomes:

10/6 - 2x = 1/6

Step 4: Subtract 10/6 from both sides to isolate the term with x.

10/6 - 10/6 - 2x = 1/6 - 10/6

This simplifies to:

-2x = -9/6

Step 5: Simplify the right side of the equation.

-9/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3.

-9/6 = (-3 * 3)/(2 * 3) = -3/2

The equation now becomes:

-2x = -3/2

Step 6: Divide both sides of the equation by -2 to solve for x.

(-2x)/-2 = (-3/2)/-2

This simplifies to:

x = 3/4

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

Answer 3

[AI-generated answer — Explain Bot]

To find the solution of the equation:

1. Start by distributing the 2 to the terms inside the parentheses:
5/3 - 2x = 1/6

2. Next, get rid of the fraction by multiplying both sides of the equation by 6. This will clear the fractions:
6 * (5/3) - 6 * (2x) = 6 * (1/6)

After multiplying, the equation will become:
(30/3) - 12x = 1

3. Simplify the equation:
10 - 12x = 1

4. Isolate the variable term (in this case, -12x) by subtracting 10 from both sides of the equation:
10 - 10 - 12x = 1 - 10

This results in:
-12x = -9

5. Solve for x by dividing both sides of the equation by -12:
(-12x)/-12 = -9/-12

The equation simplifies to:
x = 3/4

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