Question

What is the solution of the equation 5/3−2x=1/6 ?(1 point) Responses 3/4 Start Fraction 3 over 4 End Fraction 3 3 −11/12 negative Start Fraction 11 over 12 End Fraction −11/3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the equation 5/3 - 2x = 1/6, we will first isolate the term with x by subtracting 5/3 from both sides:

-2x = 1/6 - 5/3

Next, we need to find a common denominator for 1/6 and 5/3, which is 6.

-2x = 1/6 - 10/6

Now, we can combine the fractions:

-2x = (1 - 10)/6

Simplifying the numerator:

-2x = -9/6

Dividing both sides by -2:

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

x = 9/12

Simplifying the fraction:

x = 3/4

Therefore, 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, you can follow these steps:

Step 1: Subtract 5/3 from both sides of the equation to isolate the term with x.

You will get:
-2x = 1/6 - 5/3

Step 2: Find a common denominator for 1/6 and 5/3, which is 6.

Converting 5/3 to have a denominator of 6, you get: (5/3) * (2/2) = 10/6.

Now the equation becomes:
-2x = 1/6 - 10/6

Step 3: Subtract 10/6 from 1/6.

1/6 - 10/6 = -9/6

The equation becomes:
-2x = -9/6

Step 4: Simplify by dividing both sides of the equation by -2.

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

This simplifies to:
x = 9/12

Step 5: Simplify the fraction 9/12 by dividing the numerator and the denominator by their greatest common divisor, which is 3 in this case.

Dividing both 9 and 12 by 3 gives you:
x = 3/4

Therefore, the solution to the given 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 can follow these steps:

Step 1: Isolate the variable on one side of the equation.
Start with the given equation: 5/3 - 2x = 1/6
To isolate the variable "x," we need to move all other terms to the other side of the equation.
Subtract 5/3 from both sides: 5/3 - 5/3 - 2x = 1/6 - 5/3
Simplify: - 2x = 1/6 - 5/3

Step 2: Combine the fractions on the right side of the equation.
To combine the fractions with different denominators, we need to find a common denominator.
The common denominator of 6 and 3 is 6. Rewrite the fractions with the common denominator:
- 2x = (1/6) - (5/3) becomes - 2x = (1/6) - (10/6)

Step 3: Subtract the fractions with the same denominator.
Now that both fractions have the same denominator, we can subtract them.
- 2x = (1 - 10) / 6 which simplifies to - 2x = -9/6

Step 4: Simplify and solve for x.
To solve for x, divide both sides of the equation by -2.
- 2x / -2 = (-9/6) / -2
Simplify: x = (9/6) * (1/-2)

Step 5: Simplify the expression.
To simplify the expression, multiply the numerators and denominators separately.
x = 9 * 1 / 6 * -2
Simplify: x = -9 / -12

Step 6: Further simplify the fraction if possible.
The fraction -9/-12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3.
x = -9 / -12 simplifies to x = 3/4

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