Linear Inequality Word Problems

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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 range of possible solutions rather than a single solution.

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How do you represent a situation with a linear inequality?

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To represent a situation with a linear inequality, identify the variables, the coefficients, and the constraints. Formulate the inequality based on the relationships described in the problem.

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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 solve a linear inequality?

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To solve a linear inequality, isolate the variable on one side of the inequality sign, similar to solving an equation. Remember to reverse the inequality sign when multiplying or dividing by a negative number.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality uses < or >, meaning the values cannot be equal. A non-strict inequality uses ≤ or ≥, allowing for equality.

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What is the graphical representation of a linear inequality?

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The graphical representation of a linear inequality is a shaded region on one side of a boundary line. The line is solid for ≤ or ≥ and dashed for < or >.

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How do you write an inequality for a budget constraint?

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What does it mean if a linear inequality has no solution?

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If a linear inequality has no solution, it means that there are no values for the variables that satisfy the inequality. This often occurs when the constraints contradict each other.

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How do you interpret the solution set of a linear inequality?

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The solution set of a linear inequality includes all the values that satisfy the inequality. It can be represented as a range of numbers or as a shaded area on a graph.