Question

what is the solution to the equation

-1/3x-1/6=2/9

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the solution to the equation: -1/3x - 1/6 = 2/9, we can start by simplifying the equation.

First, let's get rid of the denominators by multiplying the whole equation by the least common multiple (LCM) of 3, 6, and 9, which is 18.

18(-1/3x) - 18(1/6) = 18(2/9)
-6x - 3 = 4

Next, let's isolate the variable by moving the constant term to the other side of the equation.

-6x = 4 + 3
-6x = 7

Finally, divide both sides of the equation by -6 to solve for x.

x = 7/(-6)
x = -7/6

Therefore, the solution to the equation -1/3x - 1/6 = 2/9 is x = -7/6.

Answer 2

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

To solve the equation -1/3x - 1/6 = 2/9, we can follow these step-by-step instructions:

Step 1: Simplify the equation by finding a common denominator for the fractions on the left side. The common denominator for 3 and 6 is 6.
- So, rewrite the equation as -2/6x - 1/6 = 2/9.

Step 2: Combine the fractions on the left side.
- -2/6x - 1/6 = -3/6x.

Step 3: Rewrite 2/9 as an equivalent fraction with a denominator of 6.
- Multiply the numerator and denominator of 2/9 by 2 to get 4/18.

Step 4: Substitute the equivalent fraction into the equation.
- The equation becomes -3/6x = 4/18.

Step 5: Simplify both sides of the equation.
- Simplify -3/6x to -1/2x.
- Simplify 4/18 to 2/9.

Step 6: Rewrite the equation with simplified fractions.
- The equation becomes -1/2x = 2/9.

Step 7: Solve for x by multiplying both sides of the equation by the reciprocal of -1/2 (which is -2/1 or -2).
- Multiply the left side of the equation by -2/1: -2/1 * -1/2x = 2/9 * -2/1.
- Simplify: x = -4/9.

Therefore, the solution to the equation -1/3x - 1/6 = 2/9 is x = -4/9.

Answer 3

[AI-generated answer — Explain Bot]

To find the solution to the equation, we need to isolate the variable x. Let's go through the steps to solve this equation.

Step 1: Simplify the equation if possible.
We have -1/3x - 1/6 = 2/9. To make the equation easier to work with, we can simplify the fractions by finding a common denominator for the terms involved. In this case, the common denominator is 6. Multiplying each term by 6, we get -2x - 1 = 4/9.

Step 2: Move the constant term to the other side of the equation.
To isolate the variable x, we need to move the constant term (-1) to the right side of the equation. Adding 1 to both sides, we have -2x = 4/9 + 1.

Step 3: Add or subtract fractions if necessary.
To add the fractions, we need to find a common denominator. The common denominator is 9, so we can rewrite 1 as 9/9. Now we have -2x = 4/9 + 9/9.

Step 4: Combine the fractions.
Adding the fractions, we get -2x = (4 + 9)/9, which simplifies to -2x = 13/9.

Step 5: Solve for x.
To solve for x, we need to isolate it on one side of the equation. In this case, we can do this by dividing both sides of the equation by -2.

Dividing both sides by -2, we get x = (13/9) / -2.

Step 6: Simplify the division of fractions.
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, x = (13/9) * (-1/2).

Step 7: Calculate the final answer.
Multiplying the fractions, we get x = -13/18.

So, the solution to the equation -1/3x - 1/6 = 2/9 is x = -13/18.