Question

How do you solve \[9x - 4 = 32 + 5x\] ?

Answer 1

Hint: We have been an equation with two expressions containing a single variable $x$ in the first order. Such equations are known as linear equations in one variable. To solve the equation means finding such value of $x$ which satisfies the given equation, i.e. LHS = RHS. We can transfer the terms of the variable to the left and then use simple arithmetic operations to solve the equation.

Complete step by step solution:
We have to solve the equation \[9x - 4 = 32 + 5x\] .
This is a linear equation in one variable $x$. To solve the equation means finding the value of $x$ which satisfies the equation.
First we will transfer the terms containing the variable to the left side of the equation and all other terms to the right side.
 \[
  9x - 4 = 32 + 5x \\
   \Rightarrow 9x - 5x = 32 + 4 \;
 \]
Now we will use arithmetic operations to simplify further.
 \[
  9x - 5x = 32 + 4 \\
   \Rightarrow 4x = 36 \;
 \]
We can divide both sides by $4$.
 \[
   \Rightarrow \dfrac{{4x}}{4} = \dfrac{{36}}{4} \\
   \Rightarrow x = 9 \;
\]
Thus, we get the value \[x = 9\] .
Hence, the solution to the given equation \[9x - 4 = 32 + 5x\] is \[x = 9\] .
So, the correct answer is “ \[x = 9\] ”.

Note: We solved the given equation to find the value of the unknown variable. While transferring the terms to the other side in an equation, the sign of arithmetic operation inverts, i.e. ‘+’ becomes ‘-’ and vice-versa. We can add, subtract, multiply or divide both the sides of the equation by the same number. Since the given equation was in first order, we get only one value of $x$ as the result. We can check our solution by putting the value of $x$ in the given equation. If LHS=RHS, the result is correct.