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 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 \(x = 0\), \(y = 2(0)-1=-1\), so we have the point \((0, -1)\). When \(x = 3\), \(y = 2(3)-1 = 5\), so we have the point \((3, 5)\). We can plot these two points and draw a line through them for \(y = 2x - 1\). For \(y = 5\), this is a horizontal line that passes through all points with \(y\)-coordinate 5.

Step2: Find the intersection point

The solution to the equation \(2x - 1 = 5\) is the \(x\)-coordinate of the intersection point of the two graphs \(y = 2x - 1\) and \(y = 5\). From the points we found earlier, we saw that when \(x = 3\), \(y = 5\) for the line \(y = 2x - 1\), and this is also on the line \(y = 5\). So the intersection point is \((3, 5)\).

Step3: Solve the equation algebraically (to confirm)

We can also solve the equation \(2x - 1 = 5\) algebraically. Add 1 to both sides: \(2x-1 + 1=5 + 1\), which simplifies to \(2x=6\). Then divide both sides by 2: \(\frac{2x}{2}=\frac{6}{2}\), so \(x = 3\).

Answer:

The solution to the equation \(2x - 1 = 5\) is \(x = 3\).