Question

How do you solve the linear equation $9w-7=12w-13$?

Answer 1

Hint: The above equation is in a linear form or we can say it is a linear equation in one variable. The linear equations in one variable is an equation which is expressed in the form of $ax+b=0$, where $a,b$ are two integers and not equals to zero and $x$ is a variable and has only one solution. And the order of the variables in the linear equation is always one.

Complete step by step solution:
Now the given linear equation is:
$\Rightarrow 9w-7=12w-13$
Now the above equation is exactly not looking like in a linear form $ax+b=0$, so for this first we will simplify the above equation.
Now, step by step we will simplify the given equation.
The given equation is:
$\Rightarrow 9w-7=12w-13$
Now add $7$ on both side of the equation, then we get
$\Rightarrow 9w-7+7=12w-13+7$
Now in the left side of the equation both $7$ get cancel out because they are of opposite sign and in the right by subtracting $7$ from $13$ we get
$\Rightarrow 9w=12w-6$
Now add $6$ on both side of the equation, we get
$\begin{align}
  & \Rightarrow 9w+6=12w-6+6 \\
 & \Rightarrow 9w+6=12w \\
\end{align}$
Now we will subtract $9w$ on both side of the equation, then we get
$\Rightarrow 9w-9w+6=12w-9w$
Now more simplifying, we get
$\Rightarrow 3w=6$
Now divide the both side of the equation by $3$, we get
$\Rightarrow w=2$
Hence we get one solution of the given linear equation $9w-7=12w-13$ is $w=2$.

Note: Now we can check our answer too by simply just putting the solution of the above equation $9w-7=12w-13$ which is $w=2$. And then we will check if both sides of the equation are equal or not.
Now the given equation is:
$\Rightarrow 9w-7=12w-13$
Now put the value $w=2$in the above equation we get,
$\begin{align}
  & \Rightarrow 9\left( 2 \right)-7=12\left( 2 \right)-13 \\
 & \Rightarrow 18-7=24-13 \\
 & \Rightarrow 11=11 \\
\end{align}$
Hence we get the both sides of the equation equal. It means our solution is correct which is $w=2$.