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Use the graph to solve the equation and inequality.

Write the solution to the inequality in interval notation. a. 3x
- 1 = 2x - 2 b. 3x - 1 < 2x - 2

1 Answer

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Final answer:

To solve the equation and inequality using the graph, we need to isolate the variable x. We subtract and add terms on both sides of the equation/inequality to find the solution. For the equation, the solution is x = -1. For the inequality, the solution is x < -1.

Step-by-step explanation:

a. 3x - 1 = 2x - 2:

To solve this equation, we need to isolate the variable x. First, we can remove 2x from both sides of the equation by subtracting 2x. This gives us 3x - 2x - 1 = 2x - 2 - 2x, which simplifies to x - 1 = -2. Next, we add 1 to both sides of the equation to get x - 1 + 1 = -2 + 1, which simplifies to x = -1.

b. 3x - 1 < 2x - 2:

We can solve this inequality in a similar way. First, subtract 2x from both sides of the inequality to get 3x - 2x - 1 < 2x - 2 - 2x. This simplifies to x - 1 < -2. Next, add 1 to both sides of the inequality to get x - 1 + 1 < -2 + 1, which simplifies to x < -1.

Learn more about Solving Equations and Inequalities

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