Math Problem Statement

1.2 Given the following linear inequality: βˆ’ π‘₯ ≀ 2 1.2.1 Solve the linear inequality. (2) 1.2.2 Represent your solution on a number line.

Solution

Here is the number line representation of the inequality xβ‰₯βˆ’2x \geq -2. The closed dot at βˆ’2-2 indicates inclusion, and the shading to the right represents values greater than βˆ’2-2.

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Related Questions:

  1. How do we solve inequalities when dividing by a negative number?
  2. What is the difference between strict (>,<>, <) and non-strict (β‰₯,≀\geq, \leq) inequalities?
  3. How can we check if a solution to an inequality is correct?
  4. What are some real-life applications of inequalities?
  5. How do we graph compound inequalities on a number line?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Inequalities
Number Line Representation

Formulas

Rearranging inequalities: If -x ≀ 2, then x β‰₯ -2 by multiplying both sides by -1 and flipping the inequality sign.

Theorems

Rule of inequalities: When multiplying or dividing by a negative number, the inequality sign must be flipped.

Suitable Grade Level

Grades 6-8