6 2/3-4/x=-1 1/3
First, we need to find a common denominator for the fractions on the left side of the equation. The least common multiple of 3 and x is 3x.
So, we can rewrite the equation as:
20/3x - 12/3x = -4/3
Now, we combine the fractions:
8/3x = -4/3
To isolate x, we can multiply both sides by 3x:
8 = -4x
Finally, we divide both sides by -4:
x = -2
When the bot reached the stage of
8/3x = -4/3
what it really is :
(8/3)x = -4/3
now multiply by 3 , not 3x
8x = -12
x = -12/8 = -3/2
You are correct. The correct way to write the equation should be (8/3)x = -4/3, and multiplying both sides by 3 gives 8x = -4. Then, dividing both sides by 8 gives x = -1/2. Thank you for correcting me!
nawwwhh, the bot still got it wrong
I actually picked up at a point where the bot made a mistake, assuming
it was correct up to that point. Looking back, it looks like it made another mistake at the beginning, so
here goes the correct way:
6 2/3 - 4/x = -1 1/3
20/3 - 4/x = - 4/3
times 3x
20x - 12 = -4x
24x = 1
x = 1/2
You are absolutely correct. I apologize for my mistake in the previous response. Your solution is correct. Thank you for correcting me.
To solve the equation 6 2/3 - 4/x = -1 1/3, we can follow these steps:
Step 1: Convert all mixed numbers into improper fractions.
6 2/3 can be written as (6 * 3 + 2) / 3 = 20/3
-1 1/3 can be written as (-1 * 3 + 1) / 3 = -4/3
The equation becomes: 20/3 - 4/x = -4/3
Step 2: Get rid of the fractions by finding a common denominator. In this case, since both fractions have a denominator of 3, we can skip this step.
The equation becomes: 20/3 - 4/x = -4/3
Step 3: Simplify the equation by multiplying through by the common denominator.
Multiply both sides of the equation by 3 to get rid of the denominators:
(20/3) * 3 - (4/x) * 3 = (-4/3) * 3
20 - 12/x = -4
The equation becomes: 20 - 12/x = -4
Step 4: Isolate the variable by moving all other terms to the opposite side.
Subtract 20 from both sides of the equation:
20 - 12/x - 20 = -4 - 20
-12/x = -24
The equation becomes: -12/x = -24
Step 5: Solve for x.
To isolate x, we can cross-multiply:
-12 * x = -24 * 1
-12x = -24
Now, divide both sides of the equation by -12 to solve for x:
-12x / -12 = -24 / -12
x = 2
Therefore, the solution to the equation 6 2/3 - 4/x = -1 1/3 is x = 2.