Math Problem Statement

Solve for xx and graph the solution on the number line below. minus, 24, is less than or equal to, minus, 3, x, minus, 3, or, minus, 39, is greater than, minus, 3, x, minus, 3 −24≤−3x−3or −39>−3x−3

Solution

The graph above shows the solution to the inequality. As you can see:

  • The region to the left of 7 (with a closed circle) represents x7x \leq 7.
  • The region to the right of 12 (with an open circle) represents x>12x > 12.

Would you like any further details or clarifications?

Here are 5 related questions for practice:

  1. Solve the inequality 5x+419-5x + 4 \geq 19.
  2. Graph the solution to 2x1>72x - 1 > 7 on a number line.
  3. What happens to an inequality when both sides are multiplied by a negative number?
  4. How would the solution change if the inequality was 24<3x3-24 < -3x - 3 instead of 243x3-24 \leq -3x - 3?
  5. Solve 2x+511 or x3>1-2x + 5 \leq 11 \text{ or } x - 3 > 1.

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

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Math Problem Analysis

Mathematical Concepts

Inequalities
Linear Equations
Graphing on Number Line

Formulas

Inequality solving process: ax + b ≤ c
Reversing the inequality when multiplying/dividing by a negative number

Theorems

Properties of Inequalities
Transposition and solving of linear inequalities

Suitable Grade Level

Grades 8-10