Solving Multistep Inequalities

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What is a multistep inequality?

Back

A multistep inequality is an inequality that requires more than one step to solve, often involving operations such as addition, subtraction, multiplication, or division.

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How do you isolate a variable in an inequality?

Back

To isolate a variable in an inequality, perform inverse operations on both sides of the inequality, ensuring to reverse the inequality sign when multiplying or dividing by a negative number.

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What is the difference between solving an equation and solving an inequality?

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When solving an equation, the goal is to find a specific value for the variable. In contrast, solving an inequality results in a range of values that satisfy the inequality.

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What does the inequality symbol '>' mean?

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'>' means 'greater than', indicating that the value on the left side is larger than the value on the right side.

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What does the inequality symbol '<' mean?

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'<'' means 'less than', indicating that the value on the left side is smaller than the value on the right side.

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What does the inequality symbol '≤' mean?

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'≤' means 'less than or equal to', indicating that the value on the left side is either smaller than or equal to the value on the right side.

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What does the inequality symbol '≥' mean?

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'≥' means 'greater than or equal to', indicating that the value on the left side is either larger than or equal to the value on the right side.

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How do you graph a solution to an inequality on a number line?

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To graph a solution to an inequality, use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the region that represents the solution set.

Front

What is the first step in solving the inequality -3 - 6(4x + 6) > -111?

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The first step is to distribute -6 to both terms inside the parentheses: -3 - 24x - 36 > -111.

Front

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

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The solution is x < -4.