Question

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 the equation as a function

We can rewrite the equation \(2x - 1 = 5\) as two functions: \(y = 2x - 1\) and \(y = 5\). To graph \(y = 2x - 1\), we can find two points. When \(x = 0\), \(y = 2(0)-1=-1\). When \(x = 3\), \(y = 2(3)-1 = 5\). So the line \(y = 2x - 1\) passes through \((0, - 1)\) and \((3,5)\). The line \(y = 5\) is a horizontal line parallel to the \(x\)-axis passing through \(y = 5\) on the \(y\)-axis.

Step2: Find the intersection point

The solution of the equation \(2x - 1 = 5\) is the \(x\)-coordinate of the intersection point of the two lines \(y = 2x - 1\) and \(y = 5\). From the points we found for \(y = 2x - 1\), when \(y = 5\), \(x = 3\). Also, we can solve the equation algebraically:
Start with \(2x-1 = 5\).
Add 1 to both sides: \(2x-1 + 1=5 + 1\), which simplifies to \(2x=6\).
Divide both sides by 2: \(\frac{2x}{2}=\frac{6}{2}\), so \(x = 3\).

Answer:

\(x = 3\)