Solving Inequalities and Their Properties

The video tutorial covers solving inequalities involving negative numbers. It explains the rule of flipping the inequality sign when multiplying or dividing by a negative number. The instructor provides multiple examples, demonstrating how to solve inequalities with negative coefficients, reversed coefficients, and decimals. Each example is illustrated with a number line representation to enhance understanding.

What is the special rule for inequalities when dealing with negative numbers?

• Ignore the negative sign

• Flip the inequality sign when multiplying or dividing by a negative number

• Subtract the negative number from both sides

• Add the negative number to both sides

In the inequality -4b + 9 ≤ -7, what is the first step to solve for b?

• Multiply both sides by -4

• Add 9 to both sides

• Subtract 9 from both sides

• Divide both sides by -4

After solving -4b ≤ -16, what is the value of b?

• b ≥ 4

• b ≤ -4

• b ≤ 4

• b ≥ -4

How is the solution b ≥ 4 represented on a number line?

• A line starting at -4 and going to the left

• A line starting at -4 and going to the right

• A line starting at 4 and going to the right

• A line starting at 4 and going to the left

In the inequality -x/3 - 10 ≥ 11, what is the first step to solve for x?

• Add 10 to both sides

• Subtract 10 from both sides

• Multiply both sides by 3

• Divide both sides by 3

After solving -x/3 ≥ 21, what is the value of x?

• x ≤ -63

• x ≥ 63

• x ≥ -63

• x ≤ 63

In the inequality 9 - 3t ≥ -21, what is the first step to solve for t?

• Multiply both sides by 3

• Add 9 to both sides

• Subtract 9 from both sides

• Divide both sides by 3

After solving -3t ≥ -30, what is the value of t?

• t ≤ 10

• t ≥ 10

• t ≤ -10

• t ≥ -10

In the inequality -3.6 ≥ -0.38 + 1.2, what is the first step to solve for the variable?

• Multiply both sides by 0.38

• Subtract 1.2 from both sides

• Add 1.2 to both sides

• Divide both sides by 0.38

After solving -3.6 ≥ -0.38 + 1.2, what is the value of the variable?

• Variable ≤ -16

• Variable ≥ -16

• Variable ≤ 16

• Variable ≥ 16