Solving Linear Equations and Inequalities

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What is a linear equation?

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A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

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How do you solve a linear equation?

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To solve a linear equation, isolate the variable on one side of the equation using inverse operations (addition, subtraction, multiplication, division) until the variable is alone.

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What does it mean to solve an inequality?

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Solving an inequality involves finding the values of the variable that make the inequality true, often resulting in a range of possible solutions.

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What is the difference between an equation and an inequality?

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An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

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What does the symbol '≤' mean?

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

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What does the symbol '≥' mean?

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The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be either 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 equation as a line. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Then shade the region that satisfies the inequality.

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What is the solution set of an inequality?

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The solution set of an inequality is the set of all values that satisfy the inequality, often represented on a number line or graph.

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What is an absolute value equation?

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An absolute value equation is an equation that contains an absolute value expression, such as |x| = a, where a is a non-negative number.

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How do you solve an absolute value equation?

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To solve an absolute value equation, set up two separate equations: one for the positive case and one for the negative case, then solve each equation.