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TestingSATInequalities 20 Flashcards 
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Card: 1 / 20 
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What is an inequality? |
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An inequality is a mathematical statement that compares two expressions using inequality symbols like <, >, ≤, or ≥. For example, x + 3 > 5 means that x must be greater than 2. Hint: Pay attention to whether the inequality includes equality (≤ or ≥) or not. |
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Card: 3 / 20
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What is the rule for multiplying or dividing both sides of an inequality by a negative number? |
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When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. For example, if -2x < 6, then x > -3. Hint: Always remember to flip the inequality sign when dealing with negative numbers. |
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Card: 5 / 20
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What is a tip for solving compound inequalities? |
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When solving compound inequalities, treat each part separately and then find the intersection of the two solution sets. Hint: Focus on breaking down the compound inequality into smaller, manageable pieces. |
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Card: 7 / 20
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Solve the inequality: 3x - 4 ≥ 2x + 5. |
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Card: 8 / 20
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Subtract 2x from both sides: x - 4 ≥ 5. Then add 4 to both sides: x ≥ 9. Hint: Start by isolating the variable on one side of the inequality. |
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Card: 9 / 20
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Solve the inequality: -2(x + 3) < 8. |
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Card: 10 / 20
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Distribute -2: -2x - 6 < 8. Add 6 to both sides: -2x < 14. Divide by -2 and reverse the inequality: x > -7. Hint: Don’t forget to reverse the inequality when dividing by a negative number. |
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Card: 11 / 20
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What is the addition rule of linear inequalities? |
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The addition rule states that adding the same number to both sides of an inequality does not change the inequality. For example, if x < y, then x + a < y + a for any real number a. |
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What is the subtraction rule of linear inequalities? |
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Card: 14 / 20
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The subtraction rule states that subtracting the same number from both sides of an inequality does not change the inequality. For example, if x > y, then x - a > y - a for any real number a. |
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Card: 15 / 20
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If A < B and B < C, what can be concluded? |
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You can conclude that A < C. This is known as the transitive property of inequalities. Hint: Always check the relationships between the values to apply this property. |
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What happens to the inequality sign when both sides are multiplied by a positive number? |
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Card: 18 / 20
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The inequality sign remains the same. For example, if x < y and a > 0, then ax < ay. Hint: Ensure that the number you are multiplying by is positive to keep the direction of the inequality. |
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Card: 19 / 20
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If -5 < 2x + 1 ≤ 8, what is the solution for x? |
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Card: 20 / 20
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First, split into two parts: -5 < 2x + 1 and 2x + 1 ≤ 8. Solve each part: From -5 < 2x + 1, subtract 1: -6 < 2x, then divide by 2: -3 < x. From 2x + 1 ≤ 8, subtract 1: 2x ≤ 7, then divide by 2: x ≤ 3. So, -3 < x ≤ 3. Hint: Solve each inequality separately and find the intersection of the solutions. |
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 Completed! Keep practicing to master all of them. |
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