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Last updated date: 18th Jun 2024
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Answer
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Hint: This question is from the topic of solution of linear equation in one variable. In this question we have to solve a given linear equation in one variable $5n + 6 = - 4$. We will solve this question by manipulating the given equation $5n + 6 = - 4$ by performing addition, multiplication, subtraction and division. So solving this question requires knowledge of basic mathematics operations.

Complete step by step solution:
Let us try to solve this question in which we are asked to find the value of $n$ in the given linear equation in one variable $5n + 6 = - 4$. To solve this we try to isolate variables whose value we need to find to one side of the equation by applying basic mathematics operations such as addition, multiplication, subtraction and division.
We need to solve the equation $5n + 6 = - 4$. For solving this we have to isolate the variable $n$. To
isolate $n$ we add $ - 6$ to the both side of the given equation, to get
$5n + 6 + ( - 6) = - 4 + ( - 6)$
$5n = - 10$ $eq(1)$
Because $ - 6$ is the additive inverse of $6$, so we get $5n$ in L.H.S.
Now dividing both side of the $eq(1)$ by $5$, we get the value of $n$ equals to
$\dfrac{{5n}}{5} = \dfrac{{ - 10}}{5}$
Cancelling $5$ with $5$ and we know$ - 10 = 5 \times ( - 2)$, to get
$n = - 2$
Hence the value of $n$ in the equation $5n + 6 = - 4$ is equal to$ - 2$.

Note: While solving these types of questions in which we asked to find the solution of a linear equation in one variable. To solve we just need to isolate variables to the one side of the equation and constant terms to the other side to get the value of the unknown variable. We can also check the correctness of our solution by putting back the value from our solution into the equation.