Question

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

Explanation:

Step1: Rewrite as two functions

We split the equation into $y_1=2x-1$ and $y_2=5$.

Step2: Identify key points for $y_1$

When $x=0$, $y_1=2(0)-1=-1$. When $y_1=0$, $0=2x-1 \implies x=\frac{1}{2}$. So points are $(0,-1)$ and $(\frac{1}{2},0)$.

Step3: Graph $y_2=5$

This is a horizontal line passing through $y=5$ for all $x$.

Step4: Find intersection of the two lines

Set $2x-1=5$. Add 1 to both sides:
$2x-1+1=5+1 \implies 2x=6$
Divide by 2:
$\frac{2x}{2}=\frac{6}{2} \implies x=3$
The intersection point is $(3,5)$.

Answer:

$x=3$

To graph: Plot the line $y=2x-1$ using points $(0,-1)$ and $(\frac{1}{2},0)$, then draw the horizontal line $y=5$. Their intersection at $x=3$ is the solution.