Question

here is an equation.
$2x - 1 = 5$
draw a graph to help solve the equation. then find the solution to the equation.

Explanation:

Step1: Rewrite as two functions

We can split the equation into $y=2x-1$ and $y=5$.

Step2: Plot $y=2x-1$

Find two points: when $x=0$, $y=2(0)-1=-1$; when $x=1$, $y=2(1)-1=1$. Plot $(0,-1)$ and $(1,1)$, then draw a straight line through them.

Step3: Plot $y=5$

This is a horizontal line passing through $y=5$ for all $x$.

Step4: Find intersection

The intersection of $y=2x-1$ and $y=5$ is where $2x-1=5$. Solve for $x$:
$2x=5+1$
$2x=6$
$x=\frac{6}{2}=3$

Answer:

The solution to the equation $2x-1=5$ is $x=3$.
(Graph note: The line $y=2x-1$ intersects the horizontal line $y=5$ at the point $(3,5)$.)