Two Variable Inequality Word Problems

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What is a two-variable inequality?

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A two-variable inequality is a mathematical expression that shows the relationship between two variables using inequality symbols (such as <, >, ≤, or ≥). It represents a region on a graph where the values of the variables satisfy the inequality.

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How do you represent a word problem as a two-variable inequality?

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To represent a word problem as a two-variable inequality, identify the variables, determine the constraints or limits given in the problem, and translate these into an inequality format.

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It represents a situation where the total cost of x pounds of squash at $3 per pound and y pounds of tomatoes at $4 per pound does not exceed $10.

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What is the significance of the inequality symbol '≤' in a word problem?

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The symbol '≤' indicates that the total amount can be equal to or less than a specified limit, allowing for maximum values in constraints.

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How do you determine the feasible region for a two-variable inequality?

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To determine the feasible region, graph the inequality on a coordinate plane, shading the area that satisfies the inequality, and include the boundary line if the inequality is '≤' or '≥'.

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It represents the maximum budget of $4,500 for purchasing x monitors at $250 each and y keyboards at $50 each.

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What is the difference between '<' and '≤' in inequalities?

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The symbol '<' indicates that the value must be strictly less than the limit, while '≤' allows for the value to be equal to the limit.

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How can you express a minimum revenue requirement as an inequality?

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A minimum revenue requirement can be expressed as an inequality using '≥', indicating that the revenue must be at least a certain amount.

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It signifies that the total earnings from mowing lawns (x hours at $12.50 each) and shoveling snow (y hours at $20 each) must be at least $2,000.

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How do you interpret the solution set of a two-variable inequality?

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The solution set of a two-variable inequality consists of all the ordered pairs (x, y) that satisfy the inequality, representing all possible combinations of the variables.