Question

2x - 1 = 5
draw a graph to help solve the equation. then find the solution to the equation.
solution: x = \square

Explanation:

Step1: Rearrange to linear form

We can rewrite the equation by defining two functions: $y=2x-1$ and $y=5$.

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

When $x=0$, $y=2(0)-1=-1$; when $x=3$, $y=2(3)-1=5$. So we have points $(0,-1)$ and $(3,5)$.

Step3: Graph and find intersection

Plot $y=2x-1$ (a line through the points) and $y=5$ (a horizontal line). Their intersection is at $x=3$.

Step4: Verify algebraically

Start with the original equation:
$$2x - 1 = 5$$
Add 1 to both sides:
$$2x = 5 + 1$$
$$2x = 6$$
Divide by 2:
$$x = \frac{6}{2}$$

Answer:

$x=3$

To graph:

1. Plot the horizontal line $y=5$ (parallel to the x-axis, passing through all points where the y-value is 5).
2. Plot the line $y=2x-1$ using the points $(0,-1)$ and $(3,5)$, then draw a straight line through them. The x-coordinate of where these two lines cross is the solution, which is 3.