Solving Multi Step Inequalities in One Variable

The video tutorial covers solving two-step and multi-step inequalities in one variable. It demonstrates solving inequalities such as 8m - 12 ≤ -36 and 9 - 3m > 21, including graphing the solution sets on a number line. The tutorial also addresses solving inequalities with variables on both sides and applying the distributive property to solve complex inequalities. Key steps include adding or subtracting terms, dividing by coefficients, and reversing inequality signs when dividing by negative numbers.

What is the first step in solving the inequality 8m - 12 ≤ -36?

• Divide both sides by 8

• Multiply both sides by 8

• Subtract 12 from both sides

• Add 12 to both sides

After dividing by a negative number, what should you do with the inequality sign?

• Reverse it

• Replace it with an equal sign

• Keep it the same

• Remove it

What is the solution to the inequality 9 - 3m > 21?

• m < -4

• m > -4

• m < 4

• m > 4

What does the inequality symbol change to after dividing both sides by -3?

• <

• ≥

• >

• ≤

In the inequality 7x + 7 > 21, what is the value of x after simplifying?

• x > 3

• x > 2

• x < 2

• x < 3

How do you solve an inequality with variables on both sides?

• Apply the distributive property first

• Isolate variables on one side first

• None of the above

• Combine like terms first

If you start with the inequality 7x + 7 > 21, what is the simplified form?

• x > 2

• x < 2

• x > 14

• x < 14

What is the result of applying the distributive property to 2(x - 8)?

• x - 16

• 2x + 16

• 2x - 16

• x + 16

What is the correct graphical representation for x > 2?

• Open circle at 2, shading to the right

• Closed circle at 2, shading to the right

• Open circle at 2, shading to the left

• Closed circle at 2, shading to the left

After applying the distributive property and combining like terms, what is the next step in solving the inequality?

• Check the solution

• Graph the inequality

• Divide by the coefficient of the variable

• Add or subtract to isolate the variable term