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: Isolate the variable term

To solve the equation \(2x - 1 = 5\), first, we add 1 to both sides of the equation to isolate the term with \(x\).
\[2x - 1 + 1 = 5 + 1\]
Simplifying both sides, we get:
\[2x = 6\]

Step2: Solve for \(x\)

Next, we divide both sides of the equation \(2x = 6\) by 2 to solve for \(x\).
\[\frac{2x}{2}=\frac{6}{2}\]
Simplifying both sides, we find:
\[x = 3\]

To graphically solve this, we can consider the left - hand side as \(y = 2x-1\) and the right - hand side as \(y = 5\). The graph of \(y = 2x - 1\) is a straight line with a slope of 2 and a y - intercept of - 1. The graph of \(y = 5\) is a horizontal line. The x - coordinate of the point of intersection of these two lines will be the solution of the equation \(2x - 1=5\). When \(y = 5\), substituting into \(y = 2x-1\) gives us the same equation \(2x - 1 = 5\) which we solved algebraically, and the x - value at the intersection is 3.

Answer:

\(x = 3\)