Math Problem Statement
−x−9<−12and −20≥−x−9
Solution
We are given two inequalities to solve:
Let's solve them one by one.
Inequality 1:
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Add 9 to both sides:
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Multiply both sides by and reverse the inequality:
So, for the first inequality, .
Inequality 2:
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Add 9 to both sides:
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Multiply both sides by and reverse the inequality:
So, for the second inequality, .
Combined solution:
From both inequalities, we need to satisfy:
The solution that satisfies both conditions is .
Final Answer:
The solution to the system of inequalities is:
Would you like further details or explanations?
Here are 5 related questions:
- How do you solve systems of linear inequalities?
- What happens when you multiply or divide an inequality by a negative number?
- Can inequalities have no solution? If so, how?
- How can you graph inequalities on a number line?
- What are compound inequalities, and how are they solved?
Tip: Always remember to reverse the inequality when multiplying or dividing by a negative number!
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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