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

Step3: Graph both functions

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

Step4: Find intersection x-value

The lines intersect at $x=3$, which is the solution.

Step5: Verify algebraically

Add 1 to both sides: $2x-1+1=5+1 \implies 2x=6$
Divide by 2: $\frac{2x}{2}=\frac{6}{2} \implies x=3$

Answer:

$x=3$

(For the graph: Plot the line $y=2x-1$ using the points above, plot the horizontal line $y=5$, their intersection is at $(3,5)$, so the x-coordinate 3 is the solution.)