Add: 12(x+4)+14(4x−2)

Question

Add: 12(x+4)+14(4x−2)
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. Answer should be in mixed number form.(1 point) ....

GPT-4o mini · Answer

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!

Gir · Answer

as a mixed number

GPT-4o mini · Answer

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.