Use the properties of operations to add 9(k+1/3)+10(1/2k−1) 14k−7 14 k minus 7 14k−23 14 k minus Start Fraction 2 over 3 End Fraction 14k+13 14 k plus 13 1912k−23
To simplify the expression 9(k + 1/3) + 10(1/2k - 1) + 14k - 7 + 14k - 23 - (2/3)(14k + 13) - 19 - (12k - 23), we can use the properties of operations.
First, distribute the coefficients to each term inside the parentheses:
= 9k + 9(1/3) + 10(1/2k) - 10(1) + 14k - 7 + 14k - 23 - (2/3)(14k) - (2/3)(13) - 19 - 12k + 23
Then simplify each term:
= 9k + 3 + 5/k - 10 + 14k - 7 + 14k - 23 - 28k/3 - 26/3 - 19 - 12k + 23
Now combine like terms:
= 9k + 5/k + 28k/3 + 14k + 14k - 12k - 7 - 23 - 10 - 19 + 3 - 26/3 + 23
Next simplify the fractions:
= (27k + 5)/k + (28k + 42k - 12k)/3 - 7 - 23 - 10 - 19 + 3 - 26/3 + 23
= (27k + 5)/k + 58k/3 - 57 - 26/3 + 47
Combine like terms again:
= (27k + 5)/k + (58k - 78)/3 + 0 + 21
Finally, we can rewrite the expression as:
= (27k + 5)/k + (58k - 78)/3 + 21
= (27k + 5)/k + (58k - 78)/3 + 63/3
Therefore, the simplified expression is (27k + 5)/k + (58k - 78)/3 + 21.
USE THE ANSWERS ON THE PROBLEM BOTTTTT
Apologies for the confusion earlier. Let's simplify the expression step by step:
9(k+1/3) = 9k + 3
10(1/2k-1) = 5/k - 10
14k - 7 + 14k - 23 = 28k - 30
-(2/3)(14k + 13) = -28k/3 - 26/3
-(12k - 23) = -12k + 23
Now let's combine like terms:
9k + 3 + 5/k - 10 + 28k - 30 - 28k/3 - 26/3 + 14k + 23 - 12k
Simplifying further:
9k + 28k + 14k - 12k + 3 - 10 - 30 + 23 + 5/k - 28k/3 - 26/3
Combining like terms again:
39k - 12k + 3 - 30 + 23 + 5/k - 28k/3 - 26/3
Simplifying the constants:
27k - 4 + 5/k - 28k/3 - 26/3
To simplify further, we need to find a common denominator for (5/k) and (28k/3):
27k - 4 + (15k - 26k)/3
Combining the terms with k:
27k - 4 - 11k/3
Finally, we can rewrite the expression as:
(81k - 12 - 11k)/3
Therefore, the simplified expression is (81k - 11k - 12)/3.
14k−7 14k−2/3 14k+1/3 19 1/2k−23
WHICH OF THESE ANSWERS ARE CORRECT
To determine which of the given expressions are correct, let's evaluate each of them one by one:
1) 14k - 7: This expression is simplified and cannot be further simplified.
2) 14k - 2/3: This expression is simplified and cannot be further simplified.
3) 14k + 1/3: This expression is simplified and cannot be further simplified.
4) 19: This expression is already in its simplified form.
5) 1/2k - 23: This expression is simplified and cannot be further simplified.
Based on the simplification above, all of the given expressions are correct.
19 1/2 IS A MIXED FRACTION
You are correct, my apologies for the oversight. The expression "19 1/2" is indeed a mixed fraction. Let's convert it to an improper fraction to clarify:
To convert the mixed fraction "19 1/2" to an improper fraction, we multiply the whole number (19) by the denominator of the fraction (2) and add the numerator (1). This gives us:
19 * 2 + 1 = 38 + 1 = 39
So, "19 1/2" is equivalent to the improper fraction 39/2.
Therefore, the correct expressions are:
- 14k - 7
- 14k - 2/3
- 14k + 1/3
- 39/2
- 1/2k - 23
PICK ONE ANSWER
Based on the given expressions, the correct answer is:
- 1/2k - 23