Solving Inequalities and Their Solutions

Mrs. C explains how to solve two-step inequalities, similar to two-step equations but with special attention to inequality signs. The video covers solving inequalities like 3p + 2 ≥ -10, 5(G + 4) > 15, B / -3 + 4 < 13, 2 > 8 - 4/3H, and 8 ≤ 2/5(K + 2). Each example includes step-by-step solutions, graphing on a number line, and checking solutions. The video concludes with a real-world problem involving a cave explorer's elevation, demonstrating how to set up and solve an inequality to find the time needed to reach a certain depth.

What is the first step in solving the inequality 3p + 2 ≥ -10?

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by 3

• Multiply both sides by 3

After solving the inequality 3p + 2 ≥ -10, what is the solution for p?

• p ≥ -4

• p ≤ -4

• p ≤ 4

• p ≥ 4

What is the first step in solving the inequality 5(G + 4) > 15?

• Subtract 4 from both sides

• Add 4 to both sides

• Distribute the 5

• Divide both sides by 5

What is the solution for G in the inequality 5(G + 4) > 15?

• G < -1

• G > -1

• G > 1

• G < 1

When solving B / -3 + 4 < 13, what happens to the inequality sign when multiplying by -3?

• It stays the same

• It flips

• It becomes an equal sign

• It becomes a greater than sign

What is the solution for B in the inequality B / -3 + 4 < 13?

• B < 27

• B > 27

• B > -27

• B < -27

In the inequality 2 > 8 - 4/3H, what is the first step to isolate H?

• Add 8 to both sides

• Subtract 8 from both sides

• Multiply by 4/3

• Divide by 4/3

What is the solution for H in the inequality 2 > 8 - 4/3H?

• H < -4.5

• H > -4.5

• H < 4.5

• H > 4.5

In the cave explorer problem, what inequality represents the situation?

• -38 - 12m > -200

• -38 + 12m < -200

• -38 - 12m < -200

• -38 + 12m > -200

How many minutes will it take for the cave explorer to reach an elevation deeper than -200 ft?

• More than 13.5 minutes

• Less than 13.5 minutes

• Exactly 13.5 minutes

• More than 12.5 minutes