Solving One-Step Inequalities and Graphing Solutions

The video tutorial explains how solving inequalities differs from solving equations, emphasizing the need to flip the inequality sign when multiplying or dividing by a negative number. It covers the steps to solve one-step inequalities using inverse operations and demonstrates graphing solution sets. The tutorial includes eight example problems, illustrating the process of solving and graphing inequalities.

What is the main difference between solving inequalities and solving equations?

• You need to add a constant to both sides.

• You need to flip the inequality sign when multiplying or dividing by a negative number.

• You need to multiply both sides by a positive number.

• You need to subtract a constant from both sides.

When solving inequalities, what should you do if you multiply or divide by a negative number?

• Subtract a positive number from both sides.

• Add a negative number to both sides.

• Flip the inequality sign.

• Keep the inequality sign the same.

What is the first step in solving the inequality x + 8 > 21?

• Divide both sides by 8.

• Multiply both sides by 8.

• Subtract 8 from both sides.

• Add 8 to both sides.

In the inequality -4x > -32, what operation should be performed to isolate x?

• Multiply both sides by -4.

• Divide both sides by -4.

• Add 4 to both sides.

• Subtract 4 from both sides.

When solving the inequality x/3 ≥ -5, why is the inequality sign not flipped?

• Because the inequality sign is already correct.

• Because the number being divided is negative.

• Because the number being multiplied is positive.

• Because the variable is on the left side.

What is the solution to the inequality 7x < -35?

• x < -5

• x > -5

• x < 5

• x > 5

In the inequality x/2 ≥ -8, what operation should be performed to isolate x?

• Divide both sides by -2.

• Multiply both sides by -2.

• Divide both sides by 2.

• Multiply both sides by 2.

What does the term 'sum' indicate in the inequality 'the sum of a number and 7 is more than 11'?

• Subtraction

• Division

• Multiplication

• Addition

How do you graph the solution set for x > 4?

• Place an open circle on 4 and shade to the left.

• Place an open circle on 4 and shade to the right.

• Place a closed circle on 4 and shade to the left.

• Place a closed circle on 4 and shade to the right.

In the inequality 3x ≥ 24, what is the solution for x?

• x ≤ -8

• x ≥ -8

• x ≤ 8

• x ≥ 8