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 $y_1=2x-1$ and $y_2=5$.

Step2: Find points for $y_1=2x-1$

When $x=0$, $y_1=2(0)-1=-1$; when $x=2$, $y_1=2(2)-1=3$. So we have points $(0,-1)$ and $(2,3)$.

Step3: Graph $y_2=5$

This is a horizontal line passing through $(0,5)$.

Step4: Find intersection of the two lines

Set $2x-1=5$, solve for $x$:
Add 1 to both sides: $2x=5+1=6$
Divide by 2: $x=\frac{6}{2}=3$
The intersection point is $(3,5)$.

Answer:

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