Math Problem Statement

Solve the inequality 5a + 9 ≤ 2a + 15.

Solution

The inequality given in the image is:

5a+92a+155a + 9 \leq 2a + 15

Steps to solve the inequality:

  1. Move the variable terms to one side: Subtract 2a2a from both sides: 5a2a+9155a - 2a + 9 \leq 15 Simplifying this gives: 3a+9153a + 9 \leq 15

  2. Move the constant term to the other side: Subtract 9 from both sides: 3a1593a \leq 15 - 9 Simplifying this gives: 3a63a \leq 6

  3. Solve for aa: Divide both sides by 3: a63a \leq \frac{6}{3} a2a \leq 2

Final solution:

a2a \leq 2

Let me know if you need further clarification or details!

Here are 5 related questions you might find useful:

  1. How would you solve the inequality if it involved a negative coefficient?
  2. What is the difference between solving an inequality and an equation?
  3. Can you describe how to graph the solution a2a \leq 2 on a number line?
  4. How do the properties of inequalities change when multiplying or dividing by a negative number?
  5. Can you apply this method to solve 4x+72x+54x + 7 \geq 2x + 5?

Tip: When solving inequalities, if you multiply or divide by a negative number, always remember to reverse the inequality sign!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

Linear Inequality: ax + b ≤ cx + d

Theorems

Properties of Inequalities

Suitable Grade Level

Grades 8-10