Solving Multi-Step Inequalities: Key Concepts and Techniques

What should you do when you divide both sides of an inequality by a negative number?

• Subtract the same number from both sides

• Add the same number to both sides

• Flip the inequality symbol

• Keep the inequality symbol the same

In the inequality -4y - 23 < 19, what is the first step to isolate y?

• Divide both sides by -4

• Multiply both sides by -4

• Add 23 to both sides

• Subtract 23 from both sides

When solving the inequality 2/3x ≥ -12, what should you multiply both sides by to eliminate the fraction?

• 2

• 1/2

• 3/2

• 2/3

In the inequality 7b + 11 > 9b - 3, what is the result after subtracting 7b from both sides?

• 7b + 11 > 9b

• 2b - 3 > 11

• 7b > 9b - 3

• 11 > 2b - 3

What should you do if your variable is on the right side of the inequality?

• Reverse the entire statement

• Leave it as it is

• Subtract the variable from both sides

• Add the variable to both sides

What does it mean if you end up with a false statement like 7 < 6 when solving an inequality?

• The inequality is invalid

• There is no solution

• The inequality needs to be re-evaluated

• The solution is all real numbers

In the word problem about Nathan renting a metal detector, what inequality represents the maximum hours he can rent it?

• 15 + 2h ≤ 35

• 15 + 2h ≥ 35

• 15h + 2 ≥ 35

• 15h + 2 ≤ 35

If Andy, Bobby, and Carl's ages sum to more than their father's age of 60, and they are consecutive integers, what is the inequality for their ages?

• x + x + 2 + x + 3 > 60

• x + x + 1 + x + 3 > 60

• x + x + 1 + x + 2 < 60

• x + x + 1 + x + 2 > 60

In the problem about the triangular garden, what is the inequality to find the maximum height of the triangle?

• 1/2 * 16 * h ≤ 120

• 16 * h ≤ 120

• 16 * h ≥ 120

• 1/2 * 16 * h ≥ 120

What is the maximum height of the triangular garden if the base is 16 feet and the area can be no more than 120 square feet?

• 18 feet

• 15 feet

• 12 feet

• 10 feet