Math Problem Statement

Solve and graph the solution to each of the inequality

Solve and graph the solution to each of the inequality.

Solution

The inequality in the image appears to be:

x23x - 2 \leq 3

Let's solve the inequality:

  1. Add 2 to both sides to isolate xx: x2+23+2x - 2 + 2 \leq 3 + 2 Simplifying: x5x \leq 5

So, the solution to the inequality is:

x5x \leq 5

Graph of the Solution:

To graph this inequality on a number line:

  • Draw a number line.
  • Place a closed circle at x=5x = 5 to indicate that 5 is included in the solution (because of the "less than or equal to" sign).
  • Shade the line to the left of 5 to show that all values less than or equal to 5 are solutions.

Would you like a visual graph of this solution or further details?


Here are 5 related questions:

  1. How would you solve the inequality x+37x + 3 \leq 7?
  2. What happens if you have a strict inequality like x2<3x - 2 < 3?
  3. How do you solve and graph inequalities that involve division or multiplication by a negative number?
  4. Can you solve compound inequalities such as 2<x372 < x - 3 \leq 7?
  5. How do you graph inequalities on a coordinate plane?

Tip: Always remember to reverse the inequality symbol when multiplying or dividing both sides by a negative number.

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Math Problem Analysis

Mathematical Concepts

Inequalities
Linear Equations

Formulas

x - 2 ≤ 3

Theorems

Addition Property of Inequality

Suitable Grade Level

Grades 6-8