Question

Solve the following equation $3(n - 2) + 2(4n - 5) = 5(n + 2) + 16$

Answer 1

Hint: We are going to make use of the basic operations, The addition is the sum of given two or more than two numbers, or variables and in addition, if we sum the two or more numbers then we obtain a new frame of the number will be found, also in subtraction which is the minus of given two or more than two numbers, but here comes with the condition that in subtraction the greater number sign represented in the number will stay constant example $2 - 3 = - 1$

Complete step by step answer:
Given that the equation $3(n - 2) + 2(4n - 5) = 5(n + 2) + 16$ and then we need to find the value of the unknown variable $n$, so we will make use of the basic mathematical operations to simplify further.
Starting with the multiplication operation on both the values of the sides we get $3(n - 2) + 2(4n - 5) = 5(n + 2) + 16 \Rightarrow 3n - 6 + 8n - 10 = 5n + 10 + 16$
By the addition and subtraction operation, we get $3n + 8n - 16 = 5n + 26$
now Turing the variables on the left-hand side and also the numbers on the right-hand side we get $3n + 8n - 16 = 5n + 26 \Rightarrow 3n + 8n - 5n = 26 + 16$ while changing the values on the equals to, the sign of the values or the numbers will change.
Again by the addition and subtraction, we have, $6n = 42$ for example; $11x - 5x = x(11 - 5) = 6x$ which is also applicable for the subtraction of the variables.
Hence by the division operation, we get $6n = 42 \Rightarrow n = \dfrac{{42}}{6} = 7$
Therefore, the unknown value of the given variable is $n = 7$

Note:
The other two operations are multiplication and division operations.
Since multiplicand refers to the number multiplied. Also, a multiplier refers to multiplying the first number. Have a look at an example; while multiplying $5 \times 7$the number $5$ is called the multiplicand and the number $7$ is called the multiplier. Like $2 \times 3 = 6$ or which can be also expressed in the form of $2 + 2 + 2(3times)$
The process of the inverse of the multiplication method is called division. Like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. Like $6n = 42 \Rightarrow n = \dfrac{{42}}{6} = 7$