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 linear functions

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

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

When $x=0$, $y_1=2(0)-1=-1$; when $x=1$, $y_1=2(1)-1=1$; when $x=3$, $y_1=2(3)-1=5$

Step3: Graph the two functions

• $y_2=5$ is a horizontal line through $(0,5)$.
• $y_1=2x-1$ is a line through $(0,-1)$, $(1,1)$, and $(3,5)$.

Step4: Find intersection x-value

The lines intersect where $2x-1=5$, solve algebraically:
Add 1 to both sides: $2x - 1 + 1 = 5 + 1$ → $2x = 6$
Divide by 2: $x = \frac{6}{2} = 3$

Answer:

The solution to the equation is $x=3$
(Graph: Plot the horizontal line $y=5$ and the line $y=2x-1$; their intersection is at $(3,5)$, so the x-value is the solution.)