Math Problem Statement
4x-4<8 \quad \maroonC{\text{ AND}} \quad 9x+5>23
Solution
Let's solve the two inequalities step by step:
First inequality:
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Add 4 to both sides:
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Divide by 4:
Second inequality:
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Subtract 5 from both sides:
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Divide by 9:
Combining the two inequalities:
We have:
Thus, the solution is:
Would you like more details on this?
Here are 5 related questions for further exploration:
- How would the solution change if we had and ?
- Can you represent the solution on a number line?
- How do the rules for solving inequalities differ from solving equations?
- What would happen if one inequality had no solution?
- Can inequalities be solved using graphing techniques?
Tip: Always remember to flip the inequality sign when multiplying or dividing by a negative number!
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Linear Equations
Formulas
Linear inequality manipulation: ax + b < c
Linear inequality manipulation: ax + b > c
Theorems
Properties of inequalities
Addition and subtraction property of inequalities
Division and multiplication property of inequalities
Suitable Grade Level
Grades 7-9