Question

How do you solve for \[k\] in \[h+p=3(k-8)\]?

Answer 1

Hint: Any equation can be solved by taking all the constants to one side and all the unknowns to the other side of the equation. The constant side must be solved
step-by-step to get through the solution. We need to apply distribution law, addition, subtraction, multiplication and division operations wherever necessary in such a way to simplify the equation.

Complete step by step answer:
As per the given question, we are provided with an equation to find the value of k.
In the given equation, we need to simplify \[3(k-8)\]. We need to distribute the monomial outside the parentheses of given polynomials to each term of the polynomial. By splitting up the equation, we can expand \[3(k-8)\] into the following equation:
\[\Rightarrow 3(k)-3(8)=3k-24\]
We know that \[3\left( k \right)\] is equal to \[3k\] and \[3\left( 8 \right)\] is equal to 24.
Now, we replace the right hand side of the equation with the above equation. Then we get
 \[\Rightarrow \]\[h+p=3k-24\]
Now, we have to isolate \[3k\] by adding 24 on both sides of the equation. Then, we get
\[\Rightarrow h+p+24=3k-24+24\to h+p+24=3k\]
Now, we have to isolate k by dividing with 3 on both sides of the equation. Then, we get
\[\Rightarrow \dfrac{h+p+24}{3}=\dfrac{3k}{3}\to \dfrac{h+p+24}{3}=k\]
\[\therefore \] The value of k is \[k=\dfrac{h+p+24}{3}\].

Note:
We can rather solve the equation by shifting 3 to left side and then shifting the 8 to the left side. Now take the LCM to get the value of k. This is a three step solution.
This is also the easiest way to solve the problem.
 \[\Rightarrow h+p=3(k-8)\to \dfrac{h+p}{3}=k-8\to \dfrac{h+p}{3}+8=k\to k=\dfrac{h+p+24}{3}\]. We should avoid calculation mistakes to get the correct solution.