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

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

Step2: Find points for $y_1$

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

Step3: Graph both functions

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

Step4: Find intersection point

The lines intersect at $(3,5)$, so $x=3$ satisfies $2x-1=5$.

Step5: 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:

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