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 the graphing part: We can consider the left - hand side as a function \(y = 2x-1\) and the right - hand side as a horizontal line \(y = 5\). The solution of the equation \(2x - 1=5\) is the \(x\) - coordinate of the point of intersection of the line \(y = 2x - 1\) and the line \(y = 5\). When \(y = 5\), from \(y=2x - 1\), we substitute \(y\) and solve as above to get \(x = 3\). The line \(y = 2x-1\) has a slope of 2 and a \(y\) - intercept of \(- 1\). We can plot two points on \(y = 2x - 1\) (for example, when \(x = 0\), \(y=-1\); when \(x = 1\), \(y=2\times1 - 1=1\)) and draw the line. Then we draw the horizontal line \(y = 5\). The point where they intersect has an \(x\) - value of 3.)

Answer:

\(x = 3\)