Question

How do you solve $2x+4=6$ ?

Answer 1

Hint: We solve the problem graphically. We take the two sides of the given equation as two separate functions $y=2x+4$ and $y=6$ and draw the respective lines. The two lines will intersect at a point. The abscissa of the point where they intersect will be the required solution of the given equation. If the two lines don’t intersect anywhere, then there will be no solution of the given equation. But, this will not be feasible here as all linear equations in $x$ have a solution.

Complete step by step answer:
The given equation is
$2x+4=6....equation1$
We solve this equation using graphs. For this, we need to treat the LHS of $equation1$ as
$\Rightarrow y=2x+4....equation2$
And the RHS of $equation1$ as
$\Rightarrow y=6....equation3$
$equation2$ can be rearranged as
$\Rightarrow 2x-y=-4$
Dividing by $-4$ on both sides of the equation, we get
$\Rightarrow \dfrac{x}{-2}-\dfrac{y}{-4}=1$
Upon simplification, we get,
$\Rightarrow \dfrac{x}{-2}+\dfrac{y}{4}=1$
Comparing the above equation with the intercept form of a straight line $\dfrac{x}{a}+\dfrac{y}{b}=1$ we get,
\[\begin{align}
  & x-\operatorname{intercept}=-2 \\
 & y-\operatorname{intercept}=4 \\
\end{align}\]
Now, we plot the line shown by $equation 2$ on graph. $equation3$ is simply a line of the form \[y=\text{constant}\] .
We plot it on the graph.

As we can see from the graph, the two lines intersect at $\left( 1,6 \right)$ . That means, this point satisfies both the equations $equation2$ and $equation3$ . The abscissa of the point $\left( 1,6 \right)$ is $1$ which is the solution.
Thus, we can conclude that the solution of the given equation $2x+4=6$ is $x=1$ .

Note: We need to be careful while converting an equation of a line into intercept and should keep in mind the negative signs if there. This problem can also be solved by simple algebra. We first subtract $4$ on both sides of the equation. This gives
$\Rightarrow 2x=2$
Dividing by $2$ on both sides, we get,
$\Rightarrow x=1$
But, the graphical method gives us a better idea about the graph and develops our intuition.