Question

Solve the equation both algebraically and graphically. (Lesson 1.11)

$x-4=5x+12$

Short answer

The solution by algebraically is $x=-4$and graphically is given below:

Step-by-step solution

Step 1. Definition of the intersection point.

An intersection is a single point where two lines meet or cross each other.

Step 2. Solve equation algebraically.

We have$x-4=5x+12$

Subtract $5x$from both sides of the equation:

$\begin{array}{l}x-4-5x=5x+12-5x\\ -4x-4=12\end{array}$

Add 4 to both sides:

$\begin{array}{l}-4x-4+4=12+4\\ -4x=16\end{array}$

Divide both sides by$-4$

$\begin{array}{l}\frac{-4x}{-4}=\frac{16}{-4}\\ x=-4\end{array}$

Step 3. Solve the equation graphically.

Now, equate the left side of the equation to and the right side to .

Draw the graph:

As we can see that both lines are intersecting at $\left(-4,-8\right)$.

So, the solution is $x=-4$.