How do you solve \[32n+46=1+8n\]?

Hint: This question is from the topic of linear algebra. In this question, we will have to find the value of n. For solving this question, we will first take all the values of n to the left side of the equation and solve that equation. After that, we will take all the constant terms of the equation to the right side of the equation. After that, we will solve the equation and will get the value of n. After that, we will check if our answer is correct or not.

Complete step by step solution:
Let us solve this question.
In this question, we have to solve the given term \[32n+46=1+8n\]. That means we have to solve and find the value of n from the given term \[32n+46=1+8n\].
So, the term we have to solve is
\[32n+46=1+8n\]
After taking all the terms of n to the left side of the equation, we can write the above equation as
\[\Rightarrow 32n-8n+46=1\]
The above equation can also be written as
\[\Rightarrow 24n+46=1\]
Now, taking all the constant terms to the right side of the equation, we will get
\[\Rightarrow 24n=1-46\]
The above equation can also be written as
\[\Rightarrow 24n=-45\]
Now, dividing 24 to both sides of the equation, we will get
\[\Rightarrow n=-\dfrac{45}{24}\]
As we know that 15 multiplied by 3 is 45 and 8 multiplied by 3 is 24, so we can write the above equation as
\[\Rightarrow n=-\dfrac{3\times 15}{3\times 8}\]
The above equation can also be written as
\[\Rightarrow n=-\dfrac{15}{8}\]
Hence, we have solved the term \[32n+46=1+8n\], and got the value of n as \[-\dfrac{15}{8}\].

Note: We should have better knowledge in the topic of algebra to solve this type of question easily. If we want to check if our answer is correct or not, then we can cross-check by putting this value of n in the term \[32n+46=1+8n\]. Let us put the value of n in the equation \[32n+46=1+8n\], we will get
\[32\left( -\dfrac{15}{8} \right)+46=1+8\left( -\dfrac{15}{8} \right)\]
\[\Rightarrow \dfrac{32}{8}\left( -15 \right)+46=1+\dfrac{8}{8}\left( -15 \right)\]
The above equation can also be written as
\[\Rightarrow 4\left( -15 \right)+46=1+1\left( -15 \right)\]
\[\Rightarrow -60+46=1-15\]
The above equation can also be written as
\[\Rightarrow -14=-14\]
The equation gets equal, so our answer is correct.