Question

Solve the following equation: \[3(n - 5) = - 21\]

Answer 1

Hint: In a given question linear equation in one variable is given. To solve such questions two rules are important:
BODMAS rule i.e. first we solve our bracket, then OF, then divide, then multiply, then add and in last we perform subtraction.
Then we compare terms. It means a term containing x can be subtracted from x only. Also when you change the side of any term, its sign must also change.

Formula used: We are using phenomena of solving single variable equations. First we rearrange the equation as \[ax + b = 0\]. Then we can calculate the value of an unknown variable.

Complete Step by step solution: We can use 2 methods to solve a given linear equation.
Method 1:
The given First we will simplify our bracket here i.e.
\[3(n - 5) = - 21\]
\[ \Rightarrow 3n - 15 = - 21\][We multiply 3 with both terms of the bracket]
\[3n = - 21 + 15\]
\[ \Rightarrow 3n = - 6\]
\[\therefore n = \dfrac{{ - 6}}{3} = - 2\][Since 3 is in multiplication with n, so when we change our side it comes in denominator]
Hence, we get \[n = - 2\]
Method 2:
\[(n - 5) = \dfrac{{ - 21}}{3}\] [We divide both sides with 3]
\[ \Rightarrow (n - 5) = - 7\]
\[n = - 7 + 5\]
\[ \Rightarrow n = - 2\]

So our required answer is \[n = - 2\]

Additional information: BODMAS is an abbreviation. Its full form is
B for Bracket,
O for Order,
D for Division,
M for Multiplication,
A for Addition
S for Subtraction
It explains the order of solving an expression. If an expression contains brackets ((), {}, []) , then we use the BODMAS rule for solving expressions. Here O for order indicates powers and roots, etc. Students must solve the problem in the right order. On solving in the wrong order we get the wrong answer.

Note: Students be careful while dealing with operations on variables. You must be careful of the sign after simplification. A single error in sign leads to the wrong answer. Also, most students don’t understand ‘like terms’. So remember like terms are those in which variables and their power are the same. For example:\[2x + 3y + {x^2}\] and \[3x + 5y + 2{x^2}\]. Here\[2x\] and \[3x\] are like terms because the variable and its power is the same. So we can solve them. And while solving them the variables remain the same but their coefficient will change.