Questions: Solve the following equation using a graphical method. 2x/3 - 1 = (2x - 2)/2 + 1 Graph the left side of the equation as y₁ and the right side as y₂ on the same viewing window. Choose the correct graph below. All graphs have viewing window [-10,10] by [-10,10] with Xscl = 1 and Yscl = 1.

Solve the following equation using a graphical method. 2x/3 - 1 = (2x - 2)/2 + 1 Graph the left side of the equation as y₁ and the right side as y₂ on the same viewing window. Choose the correct graph below. All graphs have viewing window [-10,10] by [-10,10] with Xscl = 1 and Yscl = 1.
Transcript text: Solve the following equation using a graphical method. \[ \frac{2 x}{3}-1=\frac{2 x-2}{2}+1 \] Graph the left side of the equation as $y_{1}$ and the right side as $y_{2}$ on the same viewing window. Choose the correct graph below. All graphs have viewing window $[-10,10]$ by $[-10,10]$ with Xscl $=1$ and Yscl $=1$.
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Solution

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Solution Steps

Step 1: Rewrite the Equation

Rewrite the given equation in a more manageable form: \[ \frac{2x}{3} - 1 = \frac{2x - 2}{2} + 1 \]

Step 2: Simplify Both Sides

Simplify both sides of the equation: \[ \frac{2x}{3} - 1 = x - 1 + 1 \] \[ \frac{2x}{3} - 1 = x \]

Step 3: Graph the Equations

Graph the left side of the equation as \( y_1 = \frac{2x}{3} - 1 \) and the right side as \( y_2 = x \).

Step 4: Identify the Correct Graph

Compare the graphs of \( y_1 \) and \( y_2 \) to the given options. The correct graph will show the intersection of \( y_1 \) and \( y_2 \).

Final Answer

The correct graph is option A.

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