Solve Equations and Inequalities with Variables on Both Sides

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

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What is an inequality?

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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.

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How do you solve an equation with variables on both sides?

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To solve an equation with variables on both sides, you can first move all terms involving the variable to one side and constant terms to the other side, then isolate the variable.

Front

What does it mean to isolate a variable?

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Isolating a variable means rearranging the equation so that the variable is on one side by itself, making it easier to solve.

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What is the first step in solving the inequality 6x + 3 > 4x - 7?

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The first step is to subtract 4x from both sides to get 2x + 3 > -7.

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What is the solution to the inequality 7(x + 3) < 5x + 13?

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The solution is x < -4.

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How do you check if your solution to an inequality is correct?

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You can check your solution by substituting a value from the solution set back into the original inequality to see if it holds true.

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What does the symbol '≤' mean in an inequality?

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The symbol '≤' means 'less than or equal to', indicating that the value can be either less than or exactly equal to another value.

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What is the solution to the equation 5x + 15 = 10x - 40?

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The solution is x = 11.

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What is the solution to the equation -2x + 18 = 2x + 40?

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The solution is x = -5.5.