Can someone please show me (STEP BY STEP!!!!!!!!!) how to properly distribute the following:

2 + 1/7 [x - (x+6 / 7) - 2]

This is what I have:

= 2 + 1/7 ( x -x-6/7 -2)
= 2 + (x - x - 6 - 2 / 49)
= (98 + x - x - 6 - 2) / 49
= 90/49

But the answer is:

6x + 78 / 49

I believe you meant to type:

2 + 1/7 [x - (x+6)/7 - 2]
= 2 + 1/7[(7x - x - 6 - 14)/7]
= 2 + 1/7[(6x - 20)/7]
= 2 + [(6x - 20)/49]
= 98/49 + (6x - 20)/49
= (98 + 6x - 20)/49
= (6x + 78)/49

watch how you place your brackets, it is extremely important

= 2 + 1/7[(7x - x - 6 - 14)/7]

Can you explain how you distributed this part thoroughly?

Nevermind I got it

To properly distribute the expression 2 + 1/7 [x - (x+6 / 7) - 2], follow these steps:

Step 1: Simplify the expression within the parentheses

Inside the parentheses, we have (x + 6/7). To simplify this, distribute the negative sign across the terms inside the parentheses. So, it becomes -(x) - (6/7), which is -x - 6/7.

Step 2: Distribute the 1/7 to the terms inside the brackets

We have 1/7 multiplying everything inside the brackets [x - (x + 6/7) - 2]. Distribute 1/7 to each term inside the brackets.

1/7 * x = x/7
1/7 * (-x) = -x/7
1/7 * (-6/7) = -6/49
1/7 * (-2) = -2/7

After distributing, we have x/7 - x/7 - 6/49 - 2/7.

Step 3: Simplify the remaining terms

Combine like terms. In this case, x/7 and -x/7 cancel each other out, so they become zero.

Remaining terms: -6/49 - 2/7

To subtract these fractions, find a common denominator. The least common multiple of 49 and 7 is 49, so we can rewrite the fractions with a denominator of 49:

-6/49 - 2/7 = -6/49 - (2/7) * (7/7) = -6/49 - 14/49

Now, we can subtract these fractions: -6/49 - 14/49 = (-6 - 14) / 49 = -20/49.

Step 4: Combine the simplified terms

Now, combine the terms from the original expression and the simplified terms.

2 + (-20/49)

To add these fractions, find a common denominator, which is 49:

2 + (-20/49) = (2 * 49)/49 + (-20/49) = 98/49 - 20/49

Now, subtract the fractions: 98/49 - 20/49 = (98 - 20)/49 = 78/49.

Therefore, the correct answer is 2 + 78/49.

Lastly, to simplify this fraction, divide the numerator by the denominator:

2 + 78/49 = 98/49 + 78/49 = (98 + 78)/49 = 176/49.

The final answer is 176/49, or as a mixed number, 3 19/49.

So, the correct answer is (6x + 78)/49, not 90/49 as you initially calculated.