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: Isolate the variable term

To solve the equation \(2x - 1 = 5\), first add 1 to both sides of the equation. This is done to get rid of the constant term on the left side that is subtracted from the variable term.

$$ 2x - 1 + 1 = 5 + 1 $$

Simplifying both sides, we know that \(-1 + 1 = 0\) and \(5 + 1 = 6\), so the equation becomes:

$$ 2x = 6 $$

Step2: Solve for x

Now, to find the value of \(x\), we divide both sides of the equation \(2x = 6\) by 2. This is because \(x\) is being multiplied by 2, and dividing by the same number (2, which is not zero) will isolate \(x\).

$$ \frac{2x}{2} = \frac{6}{2} $$

Simplifying both sides, \(\frac{2x}{2}=x\) and \(\frac{6}{2} = 3\), so we get:

$$ x = 3 $$

(For the graphing part, we can consider the function \(y = 2x - 1\) and find where \(y = 5\). When \(y = 5\), we have the original equation. To graph \(y = 2x - 1\), we can find two points: when \(x = 0\), \(y=- 1\); when \(x = 3\), \(y=2(3)-1 = 5\). Plotting these points \((0, - 1)\) and \((3,5)\) and drawing a line through them, the x - value where \(y = 5\) is \(x = 3\), which confirms our solution.)

Answer:

\(x = 3\)