Question

How do you solve $3x-7=23$?

Answer 1

Hint: We separate the variables and the constants of the equation $3x-7=23$. We apply the binary operation of addition and subtraction for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer to equate with 0. Then we solve the linear equation to find the value of $x$.

Complete step by step answer:
The given equation $3x-7=23$ is a linear equation of $x$. we need to simplify the equation by solving the variables and the constants separately.
All the terms in the equation of $3x-7=23$ are either variable of $x$ or a constant. We first separate the variables.
We take the constants all together to solve it.
$\begin{align}
  & 3x-7=23 \\
 & \Rightarrow 3x=23+7 \\
\end{align}$
There is two such constants which are 23 and 7.
Now we apply the binary operation of addition to get
$\Rightarrow 3x=23+7=30$
The binary operation between them is an addition that gives us $3x=30$.
Now we divide both sies of the equation with 3 to get
\[\begin{align}
  & 3x=30 \\
 & \Rightarrow \dfrac{3x}{3}=\dfrac{30}{3} \\
 & \Rightarrow x=10 \\
\end{align}\]
Therefore, the final solution becomes \[x=10\].
We can also solve the equation starting it with the division.
Therefore, we divide both sides of $3x-7=23$ by 3 and get
$\begin{align}
  & \dfrac{3x-7}{3}=\dfrac{23}{3} \\
 & \Rightarrow \dfrac{3x}{3}-\dfrac{7}{3}=\dfrac{23}{3} \\
\end{align}$
We take the constants fractions together.
$\Rightarrow x=\dfrac{23}{3}+\dfrac{7}{3}$
The LCM is 3. So, we get
$\Rightarrow x=\dfrac{23}{3}+\dfrac{7}{3}=\dfrac{23+7}{3}=\dfrac{30}{3}=10$
The solution is \[x=10\].

Note:
We can verify the result of the equation $3x-7=23$ by taking the value of as $x=10$.
Therefore, the left-hand side of the equation $3x-7=23$ becomes
$3x-7=3\times 10-7=30-7=23$
Thus, verified for the equation $3x-7=23$ the solution is $x=10$.