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: Rearrange the given equation

Rewrite $2x - 1 = 5$ as two linear functions:

1. $y = 2x - 1$
2. $y = 5$

Step2: Graph $y=2x-1$

Find two points for the line:

• When $x=0$, $y=2(0)-1=-1$, so point $(0, -1)$
• When $x=1$, $y=2(1)-1=1$, so point $(1, 1)$

Plot these points and draw a straight line through them.

Step3: Graph $y=5$

This is a horizontal line that passes through all points where $y=5$ (e.g., $(0,5)$, $(3,5)$). Draw this line.

Step4: Find intersection of the lines

The solution to $2x-1=5$ is the $x$-coordinate of the point where $y=2x-1$ and $y=5$ intersect. Set $2x-1=5$:
$$2x = 5 + 1$$
$$2x = 6$$
$$x = \frac{6}{2} = 3$$
The intersection point is $(3, 5)$.

Answer:

The solution to the equation is $x=3$
(The graph will have a line $y=2x-1$ crossing the horizontal line $y=5$ at $(3, 5)$)