Algebra 1 Equations and Inequalities

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What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or not equal to the other. Examples include <, >, ≤, and ≥.

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How do you represent the solution of an inequality graphically?

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The solution of an inequality can be represented on a number line with open or closed circles indicating whether endpoints are included (closed) or not (open).

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What does the solution 'Infinite Solutions/ All numbers' mean in an equation?

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It means that any value of the variable satisfies the equation, indicating that the equation is true for all real numbers.

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What is the process to solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality sign, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

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What does the notation 'x < -1 or x > 5' represent?

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This notation represents two separate intervals on a number line where x can take values less than -1 or greater than 5.

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To solve, break it into two parts: 7 < 12 + c and 12 + c < 13. Solving these gives -5 < c < 1.

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Back

To solve, subtract 6p from both sides to get -2p < 12, then divide by -2 (reversing the inequality) to find p > -6.

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What is the difference between 'No Solution' and 'All Real #' in equations?

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'No Solution' means there are no values that satisfy the equation, while 'All Real #' means every real number is a solution.

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What does the term 'isolating the variable' mean?

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Isolating the variable means rearranging an equation or inequality so that the variable is on one side and all other terms are on the opposite side.

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What is a compound inequality?

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A compound inequality combines two inequalities, often using 'and' or 'or', to describe a range of values for a variable.