Asked by Gir
Add: 12(x+4)+14(4x−2)
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. Answer should be in mixed number form.(1 point) ....
1
2
(
𝑥
+
4
)
+
1
4
(
4
𝑥
−
2
)
. Answer should be in mixed number form.(1 point) ....
Answers
Answered by
Gir
as a mixed number
Answered by
GPT-4o mini
To simplify the expression \( 12(x+4) + 14(4x - 2) \), follow these steps:
1. Distribute the numbers outside the parentheses:
- \( 12(x + 4) = 12x + 48 \)
- \( 14(4x - 2) = 56x - 28 \)
2. Combine the results:
\[
12x + 48 + 56x - 28
\]
3. Combine the like terms:
- Combine \( 12x \) and \( 56x \):
\[
12x + 56x = 68x
\]
- Combine \( 48 \) and \( -28 \):
\[
48 - 28 = 20
\]
4. The expression simplifies to:
\[
68x + 20
\]
To express this as a mixed number, we can assume we want to express \( 20 \) in a fractional component relative to \( 68x \) assuming \( x = 1 \) when needed. However, the question does not require a specific \( x \) value.
For conciseness, if you're looking for a way to express this in a mixed number form, we see \( 20 \) can be expressed in a fraction relative to \( 68x \).
Therefore, unless a specific value for \( x \) is provided to convert coefficients into mixed numbers, the simplified polynomial is:
\[
68x + 20
\]
If \( x = 1 \) for instance,
\[
68(1) + 20 \]
\[
= 68 + 20 = 88
\]
As a mixed fraction:
\[
= 88 = 88/1 = (88/1) \text{ which is already in simplest form as an integer}
\]
It’s worth clarifying further with the specifics of representing mixed numbers in terms of polynomial coefficients. Let me know if you require details on that or something else!
1. Distribute the numbers outside the parentheses:
- \( 12(x + 4) = 12x + 48 \)
- \( 14(4x - 2) = 56x - 28 \)
2. Combine the results:
\[
12x + 48 + 56x - 28
\]
3. Combine the like terms:
- Combine \( 12x \) and \( 56x \):
\[
12x + 56x = 68x
\]
- Combine \( 48 \) and \( -28 \):
\[
48 - 28 = 20
\]
4. The expression simplifies to:
\[
68x + 20
\]
To express this as a mixed number, we can assume we want to express \( 20 \) in a fractional component relative to \( 68x \) assuming \( x = 1 \) when needed. However, the question does not require a specific \( x \) value.
For conciseness, if you're looking for a way to express this in a mixed number form, we see \( 20 \) can be expressed in a fraction relative to \( 68x \).
Therefore, unless a specific value for \( x \) is provided to convert coefficients into mixed numbers, the simplified polynomial is:
\[
68x + 20
\]
If \( x = 1 \) for instance,
\[
68(1) + 20 \]
\[
= 68 + 20 = 88
\]
As a mixed fraction:
\[
= 88 = 88/1 = (88/1) \text{ which is already in simplest form as an integer}
\]
It’s worth clarifying further with the specifics of representing mixed numbers in terms of polynomial coefficients. Let me know if you require details on that or something else!
Answered by
GPT-4o mini
I apologize for any confusion earlier. Let's express the entire expression \( 68x + 20 \) as a mixed number, but keep in mind that mixed numbers are typically used for numerical values, so in this case, we'll evaluate it as if \( x \) were to take on a specific value where the overall expression results in a numerical value.
If we treat \( x \) as a variable which could represent a specific value, we can still calculate the numerical outcome for a particular value of \( x \).
Assuming we take a specific integer value for \( x \):
If \( x = 1 \):
\[
68(1) + 20 = 68 + 20 = 88
\]
\( 88 \) can be expressed as a mixed number, but since it is already a whole number, it doesn't generally fit into standard mixed number representation (which is an integer part and a fractional part).
If \( x = 0 \):
\[
68(0) + 20 = 20
\]
This value does not contain a fractional part and is simply \( 20 \).
Now, suppose we want to create a numerical example where \( x \) is a fraction:
Let \( x = \frac{1}{2} \):
\[
68\left(\frac{1}{2}\right) + 20 = 34 + 20 = 54
\]
This can again simply be expressed as \( 54 \).
To represent the polynomial as a mixed number, for arbitrary values, let’s consider if we want to represent it as:
\[
\frac{68x + 20}{1}
\]
However, the term \( 68x + 20 \) doesn’t directly lend itself to a mixed number without substituting in a numerical value for \( x \).
If indeed you're looking to express \( 68x + 20 \) generally as a mixed number form, it will need a particular value to yield a distinct numerical mixed fraction.
In conclusion, for the polynomial \( 68x + 20 \), if you meant to get a mixed number for specific value of \( x \), please clarify the expected numerical outcome, and I can help express that properly.
If we treat \( x \) as a variable which could represent a specific value, we can still calculate the numerical outcome for a particular value of \( x \).
Assuming we take a specific integer value for \( x \):
If \( x = 1 \):
\[
68(1) + 20 = 68 + 20 = 88
\]
\( 88 \) can be expressed as a mixed number, but since it is already a whole number, it doesn't generally fit into standard mixed number representation (which is an integer part and a fractional part).
If \( x = 0 \):
\[
68(0) + 20 = 20
\]
This value does not contain a fractional part and is simply \( 20 \).
Now, suppose we want to create a numerical example where \( x \) is a fraction:
Let \( x = \frac{1}{2} \):
\[
68\left(\frac{1}{2}\right) + 20 = 34 + 20 = 54
\]
This can again simply be expressed as \( 54 \).
To represent the polynomial as a mixed number, for arbitrary values, let’s consider if we want to represent it as:
\[
\frac{68x + 20}{1}
\]
However, the term \( 68x + 20 \) doesn’t directly lend itself to a mixed number without substituting in a numerical value for \( x \).
If indeed you're looking to express \( 68x + 20 \) generally as a mixed number form, it will need a particular value to yield a distinct numerical mixed fraction.
In conclusion, for the polynomial \( 68x + 20 \), if you meant to get a mixed number for specific value of \( x \), please clarify the expected numerical outcome, and I can help express that properly.