Solving Linear Inequalities Concepts

This video tutorial covers solving linear inequalities with one variable, using the distributive property, and handling variables on both sides. It explains the process of solving inequalities similarly to equations, with the key difference being the need to flip the inequality sign when multiplying or dividing by a negative number. The tutorial includes several example problems to illustrate these concepts and provides guidance on checking solutions.

What is the first step in solving a linear inequality?

• Combine like terms on both sides

• Distribute any constants

• Move all variables to one side

• Move all constants to one side

When solving inequalities, what must you do if you multiply or divide both sides by a negative number?

• Keep the inequality sign the same

• Subtract the same number from both sides

• Flip the inequality sign

• Add the same number to both sides

In the inequality 3x - 9 ≥ 12, what is the value of x after solving?

• x ≥ 7

• x ≥ 5

• x ≥ 3

• x ≥ 4

In the inequality 4x + 14 > 2, what is the value of x after solving?

• x > -3

• x > 0

• x > -2

• x > -1

If x > -3, which of the following numbers can be substituted for x to verify the solution?

• -5

• -2

• -3

• -4

What does an open circle on a number line represent when graphing inequalities?

• The number is included in the solution

• The number is not included in the solution

• The number is the maximum value

• The number is the only solution

In the inequality -6x + 2 < -5x + 14, what is the first step to solve it?

• Add 5x to both sides

• Subtract 2 from both sides

• Divide both sides by -6

• Multiply both sides by -5

What is the solution to the inequality -x + 2 < 14 after solving?

• x < 12

• x > 12

• x < -12

• x > -12

When graphing the solution x > -12, which direction should the arrow point?

• Down

• Up

• Right

• Left

What is the solution to the inequality 3/7 * -21x + 14 < 0 after solving?

• x > -1.5

• x < -1.5

• x > 1.5

• x < 1.5