Math Problem Statement

Solve the inequality: 2x + 5 ≤ 8

Solution

Let's solve the inequality step by step:

The given inequality is:

2x+582x + 5 \leq 8

Step 1: Subtract 5 from both sides

2x+55852x + 5 - 5 \leq 8 - 5 2x32x \leq 3

Step 2: Divide both sides by 2

x32x \leq \frac{3}{2} x1.5x \leq 1.5

The answer as an inequality:

x1.5x \leq 1.5

The answer in interval notation:

(,1.5](-\infty, 1.5]

Number line:

On the number line, you would put a closed circle at 1.51.5 and shade everything to the left (towards -\infty).


Would you like further details or explanations on any part? Here are five related questions that could help expand on this:

  1. How do you solve similar inequalities when there’s multiplication or division by negative numbers?
  2. Can you graph inequalities involving more complex expressions?
  3. How do you represent compound inequalities on a number line?
  4. What is the difference between strict inequalities and non-strict inequalities?
  5. How would this inequality change if it involved absolute values?

Tip: When dividing or multiplying an inequality by a negative number, remember to flip the inequality sign!

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Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities

Formulas

Basic inequality manipulation

Theorems

Properties of inequalities

Suitable Grade Level

Grades 6-8