Question

Find the value of $x$ in \[9x + 5 = 4\left( {x - 2} \right) + 8\]

Answer 1

Hint: Here, we are required to solve the given linear equation. We will simplify the expression in RHS by using the addition and distributive property of multiplication. Then by subtracting and adding like terms of the equation we will find the required value of \[x\].

Complete step by step solution:
We have to solve the linear equation \[9x + 5 = 4\left( {x - 2} \right) + 8\].
Now, we will use the distributive property to simplify the RHS.
According to the distributive property of multiplication, if a number is multiplied to a sum of two numbers, then it is given by \[a \cdot \left( {b + c} \right) = ab + ac\]. Therefore, the above equation becomes
\[ \Rightarrow 9x + 5 = 4x - 8 + 8\]
Canceling out the like terms, we get
\[ \Rightarrow 9x + 5 = 4x\]
Subtracting \[4x\] from both the sides, we get
\[ \Rightarrow 9x - 4x + 5 = 4x - 4x\]
\[ \Rightarrow 5x + 5 = 0\]
Taking 5 common from the LHS, we get
\[ \Rightarrow 5\left( {x + 1} \right) = 0\]
Dividing 5 on both the sides, we get
\[ \Rightarrow \left( {x + 1} \right) = 0\]
Subtracting 1 on both the sides, we get
\[ \Rightarrow x = - 1\]

Therefore, the required value of \[x\] in the given equation \[9x + 5 = 4\left( {x - 2} \right) + 8\] is: \[x = - 1\].

Note:
As we can notice, the given equation to be solved is a linear equation having only one variable. A linear equation in one variable is an equation which can be written in the form of \[ax + b = 0\] where \[x\] is the variable and \[a\] and \[b\] are the two integers and both of them should not be equal to zero. Now, a linear equation in one variable has only a single variable with power 1.
This is because of the fact that if the power becomes 2 then, it would not be called as a linear equation. It would turn out to be a quadratic one and there will be two solutions for the variable.