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What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols such as <, >, ≤, or ≥.

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How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then, shade the region that satisfies the inequality.

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What does the symbol '>' indicate in a linear inequality?

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The symbol '>' indicates that the values of the variable are greater than the value on the other side of the inequality.

Front

What does the symbol '<' indicate in a linear inequality?

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The symbol '<' indicates that the values of the variable are less than the value on the other side of the inequality.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the values of the variable are greater than or equal to the value on the other side of the inequality.

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What does the symbol '≤' indicate in a linear inequality?

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The symbol '≤' indicates that the values of the variable are less than or equal to the value on the other side of the inequality.

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What is the difference between a solid line and a dashed line in graphing inequalities?

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A solid line indicates that the points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that the points on the line are not included (for < or >).

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How do you determine which side of the line to shade when graphing a linear inequality?

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To determine which side to shade, you can test a point not on the line (often (0,0) if it's not on the line) in the inequality. If the inequality holds true, shade the side containing that point.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

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How can you convert a linear inequality into slope-intercept form?

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To convert a linear inequality into slope-intercept form, isolate y on one side of the inequality, similar to how you would for an equation.