Math Problem Statement

−x−9<−12and −20≥−x−9

Solution

We are given two inequalities to solve:

  1. x9<12-x - 9 < -12
  2. 20x9-20 \geq -x - 9

Let's solve them one by one.

Inequality 1:

x9<12-x - 9 < -12

  1. Add 9 to both sides: x<12+9-x < -12 + 9 x<3-x < -3

  2. Multiply both sides by 1-1 and reverse the inequality: x>3x > 3

So, for the first inequality, x>3x > 3.


Inequality 2:

20x9-20 \geq -x - 9

  1. Add 9 to both sides: 20+9x-20 + 9 \geq -x 11x-11 \geq -x

  2. Multiply both sides by 1-1 and reverse the inequality: 11x11 \leq x x11x \geq 11

So, for the second inequality, x11x \geq 11.


Combined solution:

From both inequalities, we need to satisfy:

  • x>3x > 3
  • x11x \geq 11

The solution that satisfies both conditions is x11x \geq 11.


Final Answer:

The solution to the system of inequalities is: x11x \geq 11

Would you like further details or explanations?


Here are 5 related questions:

  1. How do you solve systems of linear inequalities?
  2. What happens when you multiply or divide an inequality by a negative number?
  3. Can inequalities have no solution? If so, how?
  4. How can you graph inequalities on a number line?
  5. What are compound inequalities, and how are they solved?

Tip: Always remember to reverse the inequality when multiplying or dividing by a negative number!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Inequalities
Linear Inequalities

Formulas

Reversing inequality when multiplying/dividing by a negative number

Theorems

Properties of inequalities
Addition property of inequality
Multiplication property of inequality

Suitable Grade Level

Grades 8-10