Solve Two-Step Inequalities

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What is a two-step inequality?

Back

A two-step inequality is an inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

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How do you solve the inequality 2x + 6 ≥ -8?

Back

To solve 2x + 6 ≥ -8, first subtract 6 from both sides to get 2x ≥ -14, then divide both sides by 2 to find x ≥ -7.

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What is the first step in solving the inequality -4x + 14 ≤ 54?

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The first step is to subtract 14 from both sides, resulting in -4x ≤ 40.

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What does the solution x < -20 represent on a number line?

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The solution x < -20 represents all numbers to the left of -20 on a number line, not including -20 itself.

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How do you graph the inequality 3 + 9k > 111?

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First, solve for k: 9k > 108, then k > 12. On a number line, draw an open circle at 12 and shade to the right.

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What is the solution to the inequality 7n - 1 > 76?

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To solve 7n - 1 > 76, add 1 to both sides to get 7n > 77, then divide by 7 to find n > 11.

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What does it mean if an inequality is written with a 'greater than or equal to' symbol (≥)?

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It means that the variable can take on values that are greater than or equal to a certain number.

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What is the difference between 'greater than' (>) and 'greater than or equal to' (≥)?

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'Greater than' (>) means the value cannot equal the number, while 'greater than or equal to' (≥) includes the number itself as a possible solution.

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How do you check your solution for an inequality?

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To check your solution, substitute the value back into the original inequality to see if it makes the inequality true.

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What is the importance of reversing the inequality sign when multiplying or dividing by a negative number?

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Reversing the inequality sign is necessary to maintain the truth of the inequality when multiplying or dividing both sides by a negative number.