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Questions and Answers
What is the expression for the word 'x 2'?
What is the expression for the word 'x 2'?
x^2
What is the inequality represented by '−4x ≥ -8'?
What is the inequality represented by '−4x ≥ -8'?
x ≤ 2
What is the inequality for the graph of 'x≤2'?
What is the inequality for the graph of 'x≤2'?
x ≤ 2
What is the inequality for the graph of 'x2'?
What is the inequality for the graph of 'x2'?
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What is the inequality for the graph of 'x≤-3'?
What is the inequality for the graph of 'x≤-3'?
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What is the inequality for the graph of 'x≥-3'?
What is the inequality for the graph of 'x≥-3'?
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What is the inequality for the graph of 'x-3'?
What is the inequality for the graph of 'x-3'?
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Study Notes
Multi-step Inequalities
- Multi-step inequalities require combining like terms and isolating the variable to solve.
- Similar to equations, but the direction of the inequality symbol (>, <, ≥, ≤) must be maintained.
- When multiplying or dividing by a negative number, the inequality symbol must be flipped.
Graphing Inequalities
- Graphing involves first determining the boundary line represented by the inequality.
- For "≤" or "≥" inequalities, the boundary line is solid, indicating that the line’s points are included.
- For "<" or ">" inequalities, the boundary line is dashed, indicating that the line’s points are excluded.
- The solution set is usually shaded toward the direction that satisfies the inequality.
Inequality Examples
- For the inequality ( -4x ≥ -8 ), to solve, divide both sides by -4 (remember to flip the inequality), resulting in ( x ≤ 2 ).
- The notation ( x ≤ 2 ) means any value of x that is less than or equal to 2 will satisfy the inequality.
- For an inequality graph of ( x ≤ 2 ), shade the region to the left of the line ( x = 2 ), including the line itself.
Specific Inequalities
- The inequality ( x ≤ -3 ) indicates that x can be any number less than or equal to -3.
- The inequality ( x ≥ -3 ) indicates that x can be any number greater than or equal to -3.
- The expression ( x - 3 ) suggests a focus on values of x related to the baseline of 3, depending on further context or operations involved.
Inequality Interpretation
- Understanding the graph of inequalities helps visualize solutions and comprehend ranges of values that satisfy the conditions set by the inequalities.
- Each inequality can also have distinct real-world implications, allowing for practical application of these mathematical concepts.
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Description
This quiz focuses on solving multi-step inequalities and graphing them effectively. Students will encounter a series of flashcards that present various inequalities and ask for the corresponding graph or solution. Test your understanding of these concepts in Algebra 1!
