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

Step2: Find points for $y=2x-1$

When $x=0$, $y=2(0)-1=-1$; when $x=3$, $y=2(3)-1=5$. So we have points $(0,-1)$ and $(3,5)$.

Step3: Graph the two functions

Plot $y=5$ (a horizontal line) and $y=2x-1$ (line through $(0,-1)$ and $(3,5)$). Their intersection is at $x=3$.

Step4: Verify algebraically

Add 1 to both sides:
$2x - 1 + 1 = 5 + 1$
$2x = 6$
Divide by 2:
$\frac{2x}{2} = \frac{6}{2}$
$x=3$

Answer:

The solution to the equation is $x=3$.
(To graph: Plot the horizontal line $y=5$, plot the line $y=2x-1$ using points like $(0,-1)$ and $(3,5)$, the intersection at $(3,5)$ gives the solution.)