Solving Inequalities in Algebra

This video tutorial from YourTeacher.com explains how to solve inequalities involving negative coefficients. It covers the steps to isolate the variable, the importance of reversing the inequality sign when dividing by a negative number, and how to graph the solution on a number line. The tutorial also demonstrates how to express the solution using set notation.

What is the main goal when solving an inequality like -3x < 12?

• To find the value of x

• To get x by itself on one side

• To add 3 to both sides

• To multiply both sides by -3

What operation is performed to isolate x in the inequality -3x < 12?

• Subtracting 3 from both sides

• Adding 3 to both sides

• Dividing both sides by -3

• Multiplying both sides by 3

What must you do to the inequality sign when you divide both sides by a negative number?

• Leave it unchanged

• Add a negative sign to it

• Switch it to the opposite direction

• Multiply it by -1

What is the solution to the inequality -3x < 12?

• x < -4

• x ≤ -4

• x > -4

• x = -4

How is the solution x > -4 represented on a number line?

• An open dot at -4 with an arrow to the left

• An open dot at -4 with an arrow to the right

• A closed dot at -4 with an arrow to the left

• A closed dot at -4 with an arrow to the right

Why do we use an open dot at -4 on the number line?

• Because x is equal to -4

• Because x is less than -4

• Because x is not a real number

• Because x is greater than -4 but not equal to -4

What does set notation for the solution x > -4 look like?

• {x | x ≤ -4}

• {x | x = -4}

• {x | x < -4}

• {x | x > -4}

What is the purpose of graphing the solution on a number line?

• To visually represent the solution

• To solve the inequality

• To find the exact value of x

• To check the solution

What does the final answer in set notation represent?

• All numbers equal to -4

• Only the number -4

• All numbers less than -4

• All numbers greater than -4

What happens if you plug a number greater than -4 back into the original inequality?

• The inequality sign switches back

• The inequality becomes an equation

• You get a true statement

• You get a false statement