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 $2x - 1 = 5$ into two linear functions:
$y_1 = 2x - 1$ and $y_2 = 5$

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

Choose $x=0$: $y_1=2(0)-1=-1$, so point $(0, -1)$
Choose $x=3$: $y_1=2(3)-1=5$, so point $(3, 5)$

Step3: Graph the two functions

• $y_2=5$ is a horizontal line passing through $(0,5)$, $(3,5)$, etc.
• Plot the points for $y_1=2x-1$ and draw the line.

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

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

Answer:

The solution to the equation is $x=3$.
(To graph: Draw the line $y=2x-1$ through $(0,-1)$ and $(3,5)$, and the horizontal line $y=5$; their intersection at $x=3$ confirms the solution.)