Question

How do you solve $5 - 9w = 23$?

Answer 1

Hint: In order to determine the value of variable $w$ in the above equation use the rules of transposing terms to transpose terms having $\left( w \right)$ on the Left-hand side and constant value terms on the Right-Hand side of the equation. Solving like terms will lead to your required result.

Complete step by step solution:
We are given a linear equation in one variable $5 - 9w = 23$. and we have to solve this equation for variable ($w$).
$ \Rightarrow 5 - 9w = 23$
Now combining like terms on both of the sides. Terms having $w$ will on the Left-Hand side of the equation and constant terms on the right-hand side .
Let’s recall one basic property of transposing terms that on transposing any term from one side to another the sign of that term gets reversed .In our case,$5$ on the left hand side will become $ - 5$ on the right hand side .
After transposing terms our equation becomes
$ \Rightarrow - 9w = 23 - 5$
Now, solving the Right-hand side, we get
$ \Rightarrow - 9w = 18$
Now dividing both sides of the with coefficient of variable $w$ i.e. $ - 9$
$
   \Rightarrow \dfrac{{ - 9w}}{{ - 9}} = \dfrac{{18}}{{ - 9}} \\
   \Rightarrow w = - 2 \\
 $
Therefore, the solution to the equation $5 - 9w = 23$ is equal to $w = - 2$.

Additional Information:
Linear Equation: A linear equation is an equation which can be represented in the form of $ax + c$ where $x$ is the unknown variable and a,c are the numbers known where $a \ne 0$. If $a = 0$ then the equation will become constant value and will no more be a linear equation
The degree of the variable in the linear equation is of the order 1.
Every Linear equation has 1 root.

Note: 1. One must be careful while calculating the answer as calculation error may come.
2. Like terms are terms which have the same variable and same exponent power.
3. Coefficients of the liked terms may differ.
4. Since the equation in this question is linear in nature , that is why the number of solutions is only 1.