Question

here is an equation.
2x - 1 = 5
draw a graph to help solve the equation. then find the solution to the

Explanation:

Step1: Rewrite as two functions

We 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 $x=1$, $y_1=2(1)-1=1$; when $x=3$, $y_1=2(3)-1=5$. So points are $(0,-1)$, $(1,1)$, $(3,5)$.

Step3: Graph $y_2=5$

This is a horizontal line passing through $(0,5)$, $(3,5)$, etc.

Step4: Find intersection point

The lines $y_1=2x-1$ and $y_2=5$ intersect at $(3,5)$. The $x$-value of this point is the solution.

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:

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