Solving Linear Inequalities Concepts

The video tutorial explains how to solve linear inequalities with negative coefficients. It covers three different inequalities, demonstrating the steps to isolate the variable and the importance of reversing the inequality sign when multiplying or dividing by a negative number. Each solution is represented on a number line, and the video emphasizes checking solutions for accuracy.

What makes linear inequalities with negative coefficients special?

• They have no solutions.

• They always have positive solutions.

• The inequality sign changes when multiplying or dividing by a negative number.

• They are solved using different methods than equations.

What is the first step in solving the inequality 5 - x < 6?

• Multiply both sides by -1.

• Subtract 5 from both sides.

• Add 6 to both sides.

• Divide both sides by 5.

After isolating -x in the inequality 5 - x < 6, what should be done next?

• Add 1 to both sides.

• Multiply both sides by -1.

• Divide both sides by 5.

• Subtract 1 from both sides.

What is the solution to the inequality 5 - x < 6?

• x = -1

• x >= -1

• x < -1

• x > -1

How is the solution x > -1 represented on a number line?

• A filled circle at -1 with an arrow pointing right.

• An open circle at -1 with an arrow pointing left.

• An open circle at -1 with an arrow pointing right.

• A filled circle at -1 with an arrow pointing left.

What happens to the inequality sign when you multiply or divide by a negative number?

• It becomes an equal sign.

• It disappears.

• It stays the same.

• It reverses.

In the inequality 5 - x < 6, what is the critical number on the number line?

• 5

• 1

• 0

• -1

What is the first step in solving the inequality 2 - 5x > -8?

• Multiply both sides by 5.

• Subtract 2 from both sides.

• Add 8 to both sides.

• Divide both sides by -5.

After isolating -5x in the inequality 2 - 5x > -8, what should be done next?

• Subtract 5 from both sides.

• Divide both sides by -5.

• Multiply both sides by -5.

• Add 5 to both sides.

What is the solution to the inequality 2 - 5x > -8?

• x > 2

• x < 2

• x >= 2

• x = 2