Inequalities and Their Solutions

The video tutorial covers solving one-step inequalities using addition and subtraction. It begins with an introduction to the concept, followed by four examples demonstrating how to solve and graph inequalities. Each example involves isolating the variable and graphing the solution on a number line. The video concludes with practice problems and solutions to reinforce the concepts learned.

What is the key point to remember when solving one-step inequalities?

• Maintain the inequality sign.

• Change the inequality to an equation.

• Always use an equal sign.

• Use a different variable.

In the inequality x - 12 > 32, what operation should be performed to isolate x?

• Divide both sides by 12.

• Multiply both sides by 12.

• Add 12 to both sides.

• Subtract 12 from both sides.

After solving x - 12 > 32, what is the solution for x?

• x = 44

• x > 44

• x > 20

• x < 44

How is the solution x > 44 represented on a graph?

• Open circle at 44, arrow to the right.

• Open circle at 44, arrow to the left.

• Closed circle at 44, arrow to the left.

• Closed circle at 44, arrow to the right.

What is the first step in solving the inequality x - 12 > 32?

• Divide both sides by 12.

• Multiply both sides by 12.

• Subtract 12 from both sides.

• Add 12 to both sides.

In the inequality y - 8 ≤ 14, what operation should be performed to isolate y?

• Add 8 to both sides.

• Subtract 8 from both sides.

• Divide both sides by 8.

• Multiply both sides by 8.

What is the solution for y in the inequality y - 8 ≤ 14?

• y ≤ 6

• y ≤ 22

• y ≥ 22

• y = 22

How is the solution y ≤ 22 represented on a graph?

• Open circle at 22, arrow to the left.

• Closed circle at 22, arrow to the right.

• Closed circle at 22, arrow to the left.

• Open circle at 22, arrow to the right.

What is the first step in solving the inequality y - 8 ≤ 14?

• Multiply both sides by 8.

• Subtract 8 from both sides.

• Divide both sides by 8.

• Add 8 to both sides.

In the inequality 16 + x < -2, what operation should be performed to isolate x?

• Subtract 16 from both sides.

• Add 16 to both sides.

• Multiply both sides by 16.

• Divide both sides by 16.