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Question

Question: How do you solve \(5n + 6 = - 4\)?...

How do you solve 5n+6=45n + 6 = - 4?

Explanation

Solution

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=45n + 6 = - 4. We will solve this question by manipulating the given equation 5n+6=45n + 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 nn in the given linear equation in one variable 5n+6=45n + 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=45n + 6 = - 4. For solving this we have to isolate the variable nn. To
isolate nn we add 6 - 6 to the both side of the given equation, to get
5n+6+(6)=4+(6)5n + 6 + ( - 6) = - 4 + ( - 6)
5n=105n = - 10 eq(1)eq(1)
Because 6 - 6 is the additive inverse of 66, so we get 5n5n in L.H.S.
Now dividing both side of the eq(1)eq(1) by 55, we get the value of nn equals to
5n5=105\dfrac{{5n}}{5} = \dfrac{{ - 10}}{5}
Cancelling 55 with 55 and we know10=5×(2) - 10 = 5 \times ( - 2), to get
n=2n = - 2
Hence the value of nn in the equation 5n+6=45n + 6 = - 4 is equal to2 - 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.