Solving Two-Step Inequalities with One Variable

This video tutorial continues the discussion on solving inequalities with one variable, focusing on two-step inequalities. It covers solving and graphing inequalities, emphasizing the importance of avoiding fractions when possible. The tutorial also explains how to handle negative fractions and the necessity of changing the inequality direction when multiplying or dividing by a negative number. The video concludes with a summary of the key points discussed.

What is the first step in solving the inequality 7H ≤ 28?

• Multiply both sides by 7

• Divide both sides by 7

• Add 4 to both sides

• Subtract 4 from both sides

After adding 4 to both sides of the inequality 7H ≤ 28, what is the next step?

• Subtract 4 from both sides

• Multiply both sides by 7

• Divide both sides by 7

• Add 7 to both sides

What is the correct graph representation for the inequality H ≤ 4?

• Open circle at 4, shading to the left

• Closed circle at 4, shading to the left

• Open circle at 4, shading to the right

• Closed circle at 4, shading to the right

Why is division by a fraction avoided initially in solving inequalities?

• It is not allowed in inequalities

• It can lead to incorrect answers

• It introduces decimals

• It makes the problem more complex

What is the simplified form of the inequality 6X ≥ 2 after dividing both sides by 6?

• X ≥ 1/2

• X ≥ 1/3

• X ≥ 1/6

• X ≥ 2/3

In the inequality Z/3 < 2, what operation is performed after adding 9 to both sides?

• Subtract 3 from both sides

• Multiply both sides by 3

• Divide both sides by 3

• Add 3 to both sides

What is the result of dividing both sides of the inequality 5T ≥ 0 by 5?

• T ≥ -5

• T ≥ 5

• T ≥ 1

• T ≥ 0

What is the first step in solving the inequality -4/5M ≤ 4?

• Divide both sides by -4/5

• Add 4 to both sides

• Multiply both sides by -5/4

• Subtract 3 from both sides

When dividing both sides of an inequality by a negative number, what must be done?

• Subtract the same number from both sides

• Change the direction of the inequality

• Multiply both sides by the reciprocal

• Add the same number to both sides

What is the result of multiplying both sides of the inequality -4/5M ≤ 4 by -5/4?

• M ≥ -5

• M ≤ -5

• M ≤ 5

• M ≥ 5