Question

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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

To solve \(2x - 1 = 5\) graphically, we can consider two functions: \(y = 2x - 1\) and \(y = 5\). The solution to the equation will be the \(x\)-value where these two graphs intersect.

Step2: Find points for \(y = 2x - 1\)

• 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 points and draw the line for \(y = 2x - 1\).

Step3: Graph \(y = 5\)

The line \(y = 5\) is a horizontal line parallel to the \(x\)-axis passing through \(y = 5\) on the \(y\)-axis.

Step4: Find the intersection

The line \(y = 2x - 1\) and \(y = 5\) intersect at the point where \(y = 5\). From the point we found earlier \((3, 5)\), we can see that the \(x\)-value at the intersection is \(3\). Alternatively, we can solve the equation algebraically to verify:
Starting with \(2x - 1 = 5\), 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:

\(x = 3\)