Question

Solve the given linear equation for x:
$8x+4=3\left( x-1 \right)+7$

Answer 1

Hint: For solving this question, as we have one linear equation in terms of one unknown variable and as in the given equation there is only one variable for example in $8x+4=3\left( x-1 \right)+7$ coefficient of $y$ is zero so, we will solve it directly to find the value of unknown variable. After that, we will also plot the equation $y=8x+4$ and $y=3\left( x-1 \right)+7$ on the graph and verify our answer.

Complete step-by-step solution -
Given:
We have to solve the equation $8x+4=3\left( x-1 \right)+7$ and find the suitable value of $x$ .
Now, we will do some simple arithmetic operations and solve the given equation $8x+4=3\left( x-1 \right)+7$ easily. And first, we will simplify the term on the left-hand side and term on the right-hand side. Then,
$\begin{align}
  & 8x+4=3\left( x-1 \right)+7 \\
 & \Rightarrow 8x+4=3x-3+7 \\
\end{align}$
Now, we will subtract $3x$ from the above equation. Then,
$\begin{align}
  & 8x+4=3x-3+7 \\
 & \Rightarrow 8x-3x+4=3x-3x+4 \\
 & \Rightarrow 5x+4=4 \\
\end{align}$
Now, we will subtract 4 from the above equation. Then,
$\begin{align}
  & 5x+4=4 \\
 & \Rightarrow 5x+4-4=4-4 \\
 & \Rightarrow 5x=0 \\
\end{align}$
Now, from the above result we conclude that, the value of $5x$ will be equal to zero, which means that the value of $x$ will be also equal to zero.
Now, form the above results we can say that if $y=8x+4$ and $y=3\left( x-1 \right)+7$ then, the value of $x=0$ and value of $y=0+4=4$ . For more clarity, we can also plot both given equations on the x-y plane and verify whether they are intersecting at point (0,4) or not. The plot is shown below:

Now, from the above figure, we can verify that the two equations $y=8x+4$ and $y=3\left( x-1 \right)+7$ of straight lines will intersect at the point A whose $x$ coordinate will be $x=0$ and $y$ coordinate will be $y=4$ .
Hence, for equation $8x+4=3\left( x-1 \right)+7$ , the suitable value of $x$ will be equal to $x=0$ .

Note: We can verify the value of x that we have obtained in the above solution is by substituting the value of x in the parent equation given in the question.
The value of x that we have obtained above is:
$x=0$
The equation given in the question is:
$8x+4=3\left( x-1 \right)+7$
Substituting the value of x in the above equation we get,
$\begin{align}
  & 8\left( 0 \right)+4=3\left( 0-1 \right)+7 \\
 & \Rightarrow 0+4=-3+7 \\
 & \Rightarrow 4=4 \\
\end{align}$