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To solve the equation \( C = \frac{3}{2}(k - 91) \) for \( k \), follow these steps:
Start by multiplying both sides by \( \frac{2}{3} \) to eliminate the fraction:
\[ \frac{2}{3}C = k - 91 \]
Next, isolate \( k \) by adding \( 91 \) to both sides:
\[ k = \frac{2}{3}C + 91 \]
Thus, the solution for \( k \) is:
\[ k = \frac{2}{3}C + 91 \]
The expression for \( k \) is:
\[ k = \frac{2}{3}C + 91 \]
This expression is already in a simplified form, combining the fraction and the constant. However, if you want to express it in a single fraction, you can find a common denominator.
To combine \( \frac{2}{3}C \) and \( 91 \) into a single fraction, convert \( 91 \) to a fraction with a denominator of \( 3 \):
\[ 91 = \frac{273}{3} \]
Now you can write:
\[ k = \frac{2C}{3} + \frac{273}{3} = \frac{2C + 273}{3} \]
So, the simplified expression for \( k \) can also be written as:
\[ k = \frac{2C + 273}{3} \]
This is another simplified form of the expression.
To express \( k \) without brackets and in a more standard form, you can rewrite the expression:
Starting from the previously simplified formula:
\[ k = \frac{2C + 273}{3} \]
There are a couple of ways you could express it in "normal form," but let’s remove the fraction and express it more explicitly:
\[ 3k = 2C + 273 \]
Now, if you're looking for \( k \) in terms of \( C \) without brackets or fractions, the first form with brackets is often more common, while the second form could represent the direct relationship without a fraction.
If you prefer \( k \) isolated and written plainly (not with fractions):
So the answer in a "normal form" without fractions is:
\[ 3k = 2C + 273 \]
Alternatively, if you want \( k \) isolated, you could express it as:
\[ k = \frac{2}{3}C + 91 \]
Both forms are valid depending on whether you wish to maintain fractions or not. Would you like me to clarify any further?
To solve the equation \( mp + mq = x \) for \( m \), follow these steps:
Factor out \( m \) from the left side of the equation:
\[ m(p + q) = x \]
Now, divide both sides by \( (p + q) \) (assuming \( p + q \neq 0 \)) to isolate \( m \):
\[ m = \frac{x}{p + q} \]
Thus, the solution for \( m \) is:
\[ m = \frac{x}{p + q} \]
The solution for \( m \) derived from the equation \( mp + mq = x \) is:
\[ m = \frac{x}{p + q} \]
In "normal form" (without fractions), we rearrange the equation. To eliminate the fraction, we can multiply both sides by \( (p + q) \):
Starting from:
\[ m = \frac{x}{p + q} \]
Multiply both sides by \( (p + q) \):
\[ m(p + q) = x \]
This is a valid form of the equation representing the same relationship, but rewritten without isolating \( m \) as a fraction.
If you are looking for either an equation or statement involving \( m \) that does not have a fraction, you can use:
\[ mp + mq = x \]
So in "normal form," we can either keep it as \( m(p + q) = x \) or return to the original relationship, depending on the context. Would you like a specific form or another type of representation?
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