Final answer:
To solve the inequality 2x - 4 > 1/2x - 1 algebraically, isolate the variable x on one side of the inequality. The solution is x > 2 1/2. The correct graph representation is x > -1/3.
Step-by-step explanation:
To solve the inequality 2x - 4 > 1/2x - 1 algebraically, we need to isolate the variable x on one side of the inequality symbol. First, we can simplify the equation by multiplying through by the denominators to get rid of the fractions. This gives us: 4x - 8 > x - 1/2. Next, we can combine like terms by subtracting x from both sides of the inequality to obtain 3x - 8 > -1/2. After that, we can isolate the x term by adding 8 to both sides of the inequality: 3x > 8 - 1/2. Simplifying further, we have 3x > 7 1/2. Finally, we divide both sides of the inequality by 3 to solve for x: x > 7 1/2 ÷ 3, which simplifies to x > 2 1/2.
To represent the solution on a number line, we draw a filled-in dot at the point 2 1/2, and draw an arrow to the right to indicate that all values greater than 2 1/2 satisfy the inequality. Therefore, the correct answer is (b) x > -1/3.