Unit 2 review - linear inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

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

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The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

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

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The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

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How do you graph a linear inequality?

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

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What is the solution set of a linear inequality?

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The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality. It is represented graphically as a shaded region on the coordinate plane.

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What is a system of linear inequalities?

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A system of linear inequalities consists of two or more linear inequalities that are considered together. The solution is the region where the shaded areas of all inequalities overlap.

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How do you determine if a point is a solution to a system of linear inequalities?

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To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the standard form of a linear inequality?

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The standard form of a linear inequality is expressed as Ax + By ≤ C or Ax + By ≥ C, where A, B, and C are constants.

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Write the linear inequality for a budget of $2,700 for textbooks costing $57 each (x) and $72 each (y).

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Front

Write the linear inequality for spending under $1,000 on trees costing $14 each (x) and bushes costing $5 each (y).

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