Final Answer:
The correct answer is x ≥ 77, thus the correct option is C.
Step-by-step explanation:
To solve the inequality 3(70 + 17) > -19 + 142, start by simplifying the expressions on both sides of the inequality. First, perform the operations within the parentheses: 3 * (70 + 17) = 3 * 87 = 261. On the right side, -19 + 142 = 123. Therefore, the inequality becomes 261 > 123.
The inequality states that 261 is greater than 123, which is true. To represent this on a number line, consider x as a variable representing any number greater than or equal to 77. As 77 is the minimum value for x where the inequality holds true, the correct representation is x ≥ 77, which means x is greater than or equal to 77.
Graphically on a number line, mark the point 77 and shade the line to the right to represent all values greater than or equal to 77. This shaded area denotes the solution set that satisfies the inequality 3(70 + 17) > -19 + 142. Therefore, the solution is x ≥ 77 (option C).