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Questions and Answers
Which inequality represents the graph shown below? Open dot on -2; to the right
Which inequality represents the graph shown below? Open dot on -2; to the right
x > -2
What is the solution for the inequality x > ---------- x - 7 > 10?
What is the solution for the inequality x > ---------- x - 7 > 10?
x > 17
What is the solution for the inequality x ≤ ------------ 3x ≤ 21?
What is the solution for the inequality x ≤ ------------ 3x ≤ 21?
x ≤ 7
What does the expression 5a - 2 represent?
What does the expression 5a - 2 represent?
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Study Notes
Multi-Step Inequalities
- An open dot on -2 indicates that the value is excluded; hence the inequality is x > -2.
- To represent the interval graphically, the shading extends to the right from -2, indicating all values greater than -2.
Solving Inequalities
- For the inequality x - 7 > 10, adding 7 to both sides leads to x > 17.
- Understanding how to isolate the variable is key for solving multi-step inequalities effectively.
Compound Inequalities
- The compound inequality 3x ≤ 21 breaks down to x ≤ 7 after dividing both sides by 3.
- This indicates that x can take any value less than or equal to 7, including 7 itself.
Expressing Inequalities
- Inequalities, like 5a - 2, may require further context or conditions to be fully understood.
- Ensure to translate any expressions into usable forms for solving or graphing.
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