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 5/3 - 2(x) = 1/6, we first need to simplify the equation.

First, let's simplify the left side of the equation:
5/3 - 2(x)

Since we have a fraction and a term in parentheses multiplied by 2, we can distribute the 2 to each term inside the parentheses:
5/3 - 2x

Next, let's find a common denominator for the fractions:
The common denominator between 3 and 6 is 6, so we rewrite the equation with a common denominator of 6:
(5/3)(2/2) - 2x = 1/6

Simplifying the first term:
(10/6) - 2x = 1/6

Now, 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)
-2x = (-9/6)

Now, let's simplify the right side of the equation:
1/6 - (10/6) = -9/6

Simplifying further:
-2x = -9/6

To get the value of x, we divide both sides of the equation by -2:
(-2x)/-2 = (-9/6)/-2
x = 9/12

The solution to the equation 5/3 - 2(x) = 1/6 is x = 9/12, which can also be simplified as x = 3/4.

Answer 2

[AI-generated answer — Explain Bot]

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

Step 1: Simplify the equation if necessary.

To simplify the equation, we can start by finding a common denominator for the fractions. The common denominator for 3 and 6 is 6.

5/3 - 2x = 1/6

Rewriting the fractions with the common denominator:

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

10 / 6 - 2x = 1 / 6

Step 2: Combine like terms.

Since both fractions now have the same denominator of 6, we can combine them.

10/6 - 2x = 1/6

Step 3: Solve for x.

To solve for x, we need to get rid of the fraction 10/6 by multiplying both sides of the equation by 6.

6 * (10/6 - 2x) = 6 * (1/6)

After multiplying:

10 - 12x = 1

Step 4: Rearrange the equation.

To isolate the variable x, we need to move the constant term to the other side of the equation.

-12x = 1 - 10

-12x = -9

Step 5: Solve for x.

To solve for x, divide both sides of the equation by -12.

-12x / -12 = -9 / -12

x = 3/4

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

Answer 3

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

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

Step 1: Distribute the 2 to the terms inside the parentheses.
5/3 - 2x = 1/6

Step 2: Get rid of the fraction by multiplying the entire equation by the common denominator, which is 6.
6 * (5/3) - 6 * (2x) = 6 * (1/6)
10 - 12x = 1

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

Step 4: Move the constant term (10) to the other side of the equation by subtracting it from both sides.
10 - 10 - 12x = 1 - 10
-12x = -9

Step 5: Solve for x by dividing both sides by -12.
-12x/-12 = -9/-12
x = 3/4

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