Solving and Graphing Inequalities

In this video, Mr. J explains how to solve and graph two-step inequalities. The process involves isolating the variable using inverse operations, similar to solving two-step equations. A key point is to remember to flip the inequality symbol when multiplying or dividing by a negative number. The video includes examples of solving inequalities and graphing the solutions on a number line, with checks to ensure the solutions are correct.

What is the first step in solving a two-step inequality?

• Graph the inequality

• Multiply both sides by a constant

• Isolate the variable using inverse operations

• Add a constant to both sides

When solving the inequality -6x + 15 ≥ 27, what operation should be performed first?

• Divide by -6

• Subtract 15

• Add 15

• Multiply by -6

Why do we flip the inequality symbol when dividing by a negative number?

• To ensure the inequality remains true

• To make the inequality easier to solve

• To simplify the equation

• To change the direction of the graph

How is the solution x ≤ -2 represented on a number line?

• With a filled circle at -2 and an arrow to the left

• With a filled circle at -2 and an arrow to the right

• With an open circle at -2 and an arrow to the left

• With an open circle at -2 and an arrow to the right

What value of x can be used to verify the solution x ≤ -2?

• -3

• 0

• 2

• -1

In the inequality n/4 - 8 > 1, what is the first step to isolate n?

• Divide by 4

• Add 8

• Subtract 8

• Multiply by 4

What is the final solution for the inequality n/4 - 8 > 1?

• n ≥ 36

• n < 36

• n ≤ 36

• n > 36

How is the solution n > 36 represented on a number line?

• With an open circle at 36 and an arrow to the left

• With a filled circle at 36 and an arrow to the right

• With an open circle at 36 and an arrow to the right

• With a filled circle at 36 and an arrow to the left

Which value of n can be used to verify the solution n > 36?

• 34

• 36

• 35

• 37

What operation is used to solve n/4 > 9?

• Subtract 4

• Multiply by 4

• Add 4

• Divide by 4