Math Problem Statement

answer the questions

Which number line shows the solution of 5x - 25 > -15?

Solution

Let's solve the inequality 5x25>155x - 25 > -15.

Step 1: Isolate the variable xx

Add 25 to both sides of the inequality:

5x25+25>15+255x - 25 + 25 > -15 + 25 5x>105x > 10

Step 2: Solve for xx

Now, divide both sides by 5:

x>105x > \frac{10}{5} x>2x > 2

Solution:

The solution to the inequality is x>2x > 2, meaning the values of xx are greater than 2.

Step 3: Match the correct graph

The number line should show an open circle at x=2x = 2 (since xx is greater than 2, but not equal to 2) and shading to the right, indicating that the values of xx are greater than 2.

Looking at the options:

  • Option A shows x>2x > 2 with an open circle at 2 and shading to the right, which matches the solution.

Therefore, Option A is the correct answer.


Do you need further details or have any questions?

Here are five related questions:

  1. How would the graph change if the inequality was 5x25155x - 25 \geq -15?
  2. What happens to the solution if the inequality sign changes to <<?
  3. Can you explain how to solve an inequality with a negative coefficient on xx?
  4. How can we graph a compound inequality like 2x+15 and x3<62x + 1 \geq 5 \text{ and } x - 3 < 6?
  5. What is the difference between solving inequalities and solving equations?

Tip: Always check if you need an open or closed circle when graphing solutions for inequalities!

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Math Problem Analysis

Mathematical Concepts

Linear Inequalities
Number Lines

Formulas

5x - 25 > -15
x > 2

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 6-8