Solving Inequalities: Key Concepts and Techniques

What does the addition property of inequality allow us to do?

• Multiply both sides of the inequality by the same number

• Add the same value to both sides of the inequality without changing its truth

• Add different values to each side of the inequality

• Subtract the same value from both sides of the inequality

If an inequality is solved by adding the same number to both sides, which property is being used?

• Multiplication property of inequality

• Subtraction property of inequality

• Division property of inequality

• Addition property of inequality

If x - 3 > -10, what is the first step to isolate x using the addition property?

• Subtract 3 from both sides

• Add 3 to both sides

• Divide both sides by 3

• Multiply both sides by -3

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

• By subtracting the solution from both sides of the inequality

• By substituting a number larger than the solution into the inequality

• By adding the solution to both sides of the inequality

• By substituting the solution back into the original equation

To solve x - 3 > -10, after adding 3 to both sides, what is the new inequality?

• x < -7

• x > -7

• x < -13

• x > -13

What does the subtraction property of inequality allow us to do?

• Subtract different values from each side of the inequality

• Add the same value to both sides of the inequality

• Multiply both sides of the inequality by the same number

• Subtract the same value from both sides of the inequality without changing its truth

If x + 8 > -15, what is the first step to isolate x using the subtraction property?

• Subtract 8 from both sides

• Add 8 to both sides

• Divide both sides by 8

• Multiply both sides by 8

What is the correct graph representation for n + 11 ≥ 20?

• A closed circle at 9 with a line extending to the right

• An open circle at 9 with a line extending to the left

• A closed circle at 9 with a line extending to the left

• An open circle at 9 with a line extending to the right

What is the solution to the inequality n + 11 ≥ 20?

• n < 9

• n > 9

• n ≤ 9

• n ≥ 9

When graphing n + 11 ≥ 20, why is a closed circle used at 9?

• Because n can be 9 or any number larger

• Because n is exactly 9

• Because n can be greater than 9

• Because n can be 9 or any number smaller