Absolute Value Inequalities and Solutions

The video tutorial covers Chapter 2, Section 6 of Algebra 1, focusing on absolute value inequalities. It begins with an introduction to the concept, explaining how to set up and solve basic absolute value inequalities. The tutorial progresses to more complex examples, demonstrating how to handle equations with additional terms and coefficients. Special cases are also discussed, highlighting scenarios where absolute values are compared to negative numbers, leading to unique solutions or no solutions. The video emphasizes the importance of understanding the properties of absolute values and their implications in inequalities.

What is the first step in solving an absolute value inequality?

• Graph the inequality

• Multiply both sides by a negative number

• Set up two separate equations

• Add a constant to both sides

When setting up equations for an absolute value inequality, what must you remember to do with the inequality sign?

• Always change it to an equal sign

• Flip it when multiplying by a negative

• Ignore it

• Keep it the same

What is the result of dividing both sides of an inequality by a negative number?

• The inequality becomes an equation

• The inequality sign flips

• The inequality sign remains the same

• The inequality sign is removed

In the inequality |x + 7| ≤ 2, what are the two equations you set up?

• x + 7 ≤ 2 and x + 7 = 2

• x + 7 ≥ 2 and x + 7 ≤ -2

• x + 7 ≤ 2 and x + 7 ≥ -2

• x + 7 = 2 and x + 7 = -2

What does a closed circle on a number line represent?

• The value is included in the solution

• The inequality is strict

• The value is not included in the solution

• The inequality is an equation

In the inequality |x + 7| ≤ 2, what is the range of x?

• -5 ≤ x ≤ 9

• -5 ≤ x ≤ -9

• -9 ≤ x ≤ -5

• -9 ≤ x ≤ 5

What is the solution to the inequality |x + 7| ≤ 2?

• -5 ≤ x ≤ 9

• x ≥ -5 or x ≤ -9

• -9 ≤ x ≤ -5

• x ≤ -5 or x ≥ -9

What is the solution to the inequality |x + 7| > 2?

• x > 9 or x < -5

• x < 5 or x > -9

• x < 9 or x > -5

• x > 5 or x < -9

What is the solution to the inequality |x + 7| < 2?

• -9 < x < 5

• -5 < x < 9

• -5 < x < -9

• -9 < x < -5

What is the first step in solving the inequality 4|2x - 5| + 1 > 21?

• Multiply both sides by 4

• Divide both sides by 4

• Subtract 1 from both sides

• Add 1 to both sides