Math Problem Statement

Solve and write interval notation for the solution set: -10 < 2x + 5 < 7. Then graph the solution set.

Solution

It looks like I need to handle the inequality in two parts separately. Let's solve each part of the compound inequality:

10<2x+5<7-10 < 2x + 5 < 7

This can be split into:

  1. 10<2x+5-10 < 2x + 5
  2. 2x+5<72x + 5 < 7

I'll solve both inequalities now.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through solving the inequality step-by-step:

We have the inequality:

10<2x+5<7-10 < 2x + 5 < 7

Step 1: Break the inequality into two parts:

  1. 10<2x+5-10 < 2x + 5
  2. 2x+5<72x + 5 < 7

Step 2: Solve the first part 10<2x+5-10 < 2x + 5

Subtract 5 from both sides: 105<2x    15<2x-10 - 5 < 2x \implies -15 < 2x Divide by 2: x>152    x>7.5x > -\frac{15}{2} \implies x > -7.5

Step 3: Solve the second part 2x+5<72x + 5 < 7

Subtract 5 from both sides: 2x<75    2x<22x < 7 - 5 \implies 2x < 2 Divide by 2: x<1x < 1

Step 4: Combine the two inequalities

7.5<x<1-7.5 < x < 1

Step 5: Write the solution in interval notation

The solution is: (7.5,1)(-7.5, 1)

Would you like help graphing this solution, or do you have any further questions?

Here are five related questions you might find useful:

  1. How do you solve compound inequalities?
  2. How do you graph inequalities on a number line?
  3. What is interval notation, and when is it used?
  4. How do inequalities differ from equations?
  5. How do we interpret strict inequalities vs. inclusive ones?

Tip: Always remember to flip the inequality sign when dividing by a negative number!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Interval Notation

Formulas

Solving Linear Inequalities
Interval Notation

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 7-10