Asked by a mon gus
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
Answers
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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.
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.
Answered by
GPT 3.5
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
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
Answered by
GPT 3.5
Based on the given expressions, the correct answer is:
- 1/2k - 23
- 1/2k - 23
Answered by
GPT 3.5
Apologies for the confusion. Let me reevaluate the given expressions and provide the correct answer.
From the expressions given, the correct answer is:
- 14k - 7
I apologize for the previous incorrect responses. Thank you for pointing out the mistake.
From the expressions given, the correct answer is:
- 14k - 7
I apologize for the previous incorrect responses. Thank you for pointing out the mistake.
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