Inequalities and Their Solutions

This video tutorial covers solving equations and inequalities, focusing on using a T-chart method. It explains how to determine correct solutions and highlights common mistakes, such as not flipping the inequality sign when multiplying or dividing by a negative number. The tutorial also applies these concepts to real-world problems, like calculating the dimensions of a rectangle and analyzing triangle perimeters.

What is the first step in solving an inequality?

• Check the answer choices

• Draw a do-undo T-chart

• Multiply both sides by zero

• Guess the solution

If x/8 > 3, what operation should be performed to isolate x?

• Add 8 to both sides

• Subtract 8 from both sides

• Divide both sides by 8

• Multiply both sides by 8

Which value of x satisfies the inequality x > 24?

• 22

• 24

• 30

• 20

What mistake did Macy make when solving x/(-12) > 7.8?

• She added 12 to both sides

• She multiplied incorrectly

• She forgot to flip the inequality symbol

• She divided by the wrong number

When multiplying or dividing by a negative number, what must you remember to do?

• Add the same number to both sides

• Subtract the same number from both sides

• Flip the inequality symbol

• Keep the inequality symbol the same

What is the solution to the inequality -100 > -5y?

• y < 20

• y > 20

• y = 20

• y < -20

In the inequality -100 > -5y, what operation is used to isolate y?

• Multiply by -5

• Divide by -5

• Add 5

• Subtract 5

What is the maximum possible length of the base of a rectangle with a height of 4 units and an area of up to 48 square units?

• 10

• 12

• 14

• 16

If the area of a rectangle is given by base times height, what inequality represents the possible lengths of the base if the area is less than or equal to 48?

• Base ≥ 12

• Base ≤ 12

• Base < 12

• Base > 12

What is the length of line segment YZ if the perimeter of the triangle is 75.3 and two sides are 20.4 each?

• 34.5

• 30.5

• 25.5

• 40.5