Math Problem Statement
answer the questions
Which number line shows the solution of 5x - 25 > -15?
Solution
Let's solve the inequality .
Step 1: Isolate the variable
Add 25 to both sides of the inequality:
Step 2: Solve for
Now, divide both sides by 5:
Solution:
The solution to the inequality is , meaning the values of are greater than 2.
Step 3: Match the correct graph
The number line should show an open circle at (since is greater than 2, but not equal to 2) and shading to the right, indicating that the values of are greater than 2.
Looking at the options:
- Option A shows 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:
- How would the graph change if the inequality was ?
- What happens to the solution if the inequality sign changes to ?
- Can you explain how to solve an inequality with a negative coefficient on ?
- How can we graph a compound inequality like ?
- 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