1/3(k+9)-7(1/6k+2)
To simplify the expression 1/3(k+9)-7(1/6k+2), we need to distribute and combine like terms.
Here's the step-by-step solution:
1/3(k+9) - 7(1/6k+2)
First, let's simplify within the parentheses.
1/3(k+9) = k/3 + 9/3 = k/3 + 3
Now let's simplify within the second parentheses.
1/6k + 2
To add them, we need a common denominator, which in this case is 6k.
The first fraction becomes (1 * k + 2 * 6) / (6k)
This simplifies to (k + 12) / (6k)
Therefore, our expression becomes:
k/3 + 3 - 7(k + 12) / (6k)
Next, let's distribute the -7 to the terms inside the second parentheses.
-7(k + 12) = -7k - 84
After distributing, our expression becomes:
k/3 + 3 - (7k + 84) / (6k)
Next, let's find a common denominator for the fractions.
The common denominator is 3 * 6k = 18k
k/3 = (k * 6k) / (18k) = 6k^2 / 18k = k^2 / 3k
So the expression now becomes:
(k^2 / 3k) + 3 - (7k + 84) / (6k)
Next, let's combine the fractions.
The second fraction can also be expressed as (7k + 84) / (6k) = (7k/6k) + (84/6k) = 7/6 + 14/k
Therefore, the expression simplifies to:
k^2 / 3k + 3 - 7/6 - 14/k
Finally, we can combine the terms with like variables:
k^2 / 3k - 14/k + 3 - 7/6
If you need further simplification for this expression, please let me know.
I need it to be simplify
To further simplify the expression k^2 / 3k - 14/k + 3 - 7/6, we can combine the terms by finding a common denominator.
The least common denominator for 3k and k is 3k.
Multiplying the first term by 1 in the form of 3k/3k gives us (k^2 * 3k) / (3k * 3k) = 3k^3 / 9k^2 = k/3.
The least common denominator for k and 6 is 6k.
Multiplying the second term by 1 in the form of 6/6 gives us (14 * 6) / (k * 6) = 84 / 6k = 14 / k.
Now our expression becomes:
k/3 - 14/k + 3 - 7/6.
To find a common denominator for 3 and 6, we multiply the first term by 2/2, giving us (k * 2) / (3 * 2) = 2k/6.
Therefore, our expression simplifies to:
2k/6 - 14/k + 3 - 7/6.
Now we need to find a common denominator for 6 and k.
Multiplying the third term by k/k gives us (3 * k) / (6 * k) = 3k / 6k = k / 2k = 1/2.
Our expression now becomes:
2k/6 - 14/k + 1/2 - 7/6.
To find a common denominator for 6 and 2, we multiply the fourth term by 3/3, giving us (7 * 3) / (6 * 3) = 21 / 18 = 7/6.
Finally, our fully simplified expression is:
2k/6 - 14/k + 1/2 - 7/6 = k/3 - 14/k + 1/2 - 7/6.
To simplify the expression 1/3(k+9) - 7(1/6k+2), we can follow the order of operations, which is often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
First, let's simplify the expression inside the parentheses:
The expression 1/6k+2 is divided into two terms, 1/6k and 2.
Next, let's simplify the multiplication and addition/subtraction:
1/3(k+9) - 7(1/6k+2) translates to the following expression:
1/3 * k + 1/3 * 9 - 7 * 1/6 * k - 7 * 2
Using the distributive property, we can multiply the numbers outside the parentheses with each term inside the parentheses:
1/3 * k + 3/3 - 7/6 * k - 14
Now we combine like terms:
1/3 * k - 7/6 * k + 3/3 - 14
To add or subtract fractions, the denominators must be the same. Therefore, we need to find a common denominator for 3 and 6. In this case, the least common multiple (LCM) is 6. So we need to convert 1/3 to 2/6:
2/6 * k - 7/6 * k + 3/3 - 14
Now we can combine like terms:
(2k - 7k)/6 + 3/3 - 14
Simplifying the numerator:
-5k/6 + 3/3 - 14
The fractions 3/3 and -14 can also be written as 1 and -14:
-5k/6 + 1 - 14
Combining the expression:
-5k/6 - 13
So, the simplified form of 1/3(k+9) - 7(1/6k+2) is -5k/6 - 13.
To simplify the expression 1/3(k + 9) - 7(1/6k + 2), we can follow these steps:
Step 1: Distribute the 7 to the terms inside the parentheses:
1/3(k + 9) - 7(1/6k + 2) = 1/3(k + 9) - 7/6k - 14
Step 2: Simplify the fractions:
1/3(k + 9) = (k + 9)/3
Step 3: Combine like terms:
(k + 9)/3 - 7/6k - 14
Since the denominators are different (3 and 6), we need to find a common denominator, which is 6. To do this, we can multiply the first fraction by 2/2:
2/2 * (k + 9)/3 = (2k + 18)/6
Now we have a common denominator of 6. Let's rewrite the original expression with the common denominator:
(2k + 18)/6 - 7/6k - 14
Step 4: Combine like terms:
(2k + 18 - 7 - 14)/6k
Simplifying further:
(2k - 3)/6k
So, the simplified expression is (2k - 3)/6k.