Algebra 1: Multi-Step Inequalities & Graphing

Questions and Answers

What is the expression for the word 'x 2'?

x^2

What is the inequality represented by '−4x ≥ -8'?

x ≤ 2

What is the inequality for the graph of 'x≤2'?

x ≤ 2

What is the inequality for the graph of 'x2'?

x^2 Signup and view all the answers

What is the inequality for the graph of 'x≤-3'?

x ≤ -3 Signup and view all the answers

What is the inequality for the graph of 'x≥-3'?

x ≥ -3 Signup and view all the answers

What is the inequality for the graph of 'x-3'?

x > 3 Signup and view all the answers

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.

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!