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

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

(For graphing: 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. To graph \(y = 2x - 1\), when \(x = 0\), \(y=-1\); when \(x = 1\), \(y=2(1)-1 = 1\); when \(x = 2\), \(y=2(2)-1 = 3\); when \(x = 3\), \(y=2(3)-1 = 5\). The graph of \(y = 5\) is a horizontal line parallel to the \(x\) - axis passing through \((0,5)\). The point of intersection of \(y = 2x - 1\) and \(y = 5\) is at \(x = 3\), which confirms our solution.)

Answer:

\(x = 3\)