Solving Absolute Value Equations and Inequalities

This video tutorial by Mr. Tarrou covers solving equations and inequalities involving absolute value functions. It starts with simple examples and progresses to more complex problems, including those with no solutions and fractional inequalities. The tutorial emphasizes the importance of isolating the absolute value function, breaking it into two parts, and checking solutions. Graphing solutions on a number line is also demonstrated.

What is the first step in solving an equation with an absolute value function?

• Add a constant to both sides

• Combine like terms

• Isolate the absolute value function

• Distribute the negative sign

When solving the absolute value equation |x| = 8, what are the two possible solutions for x?

• x = 8 and x = -8

• x = 8 and x = 0

• x = 8 and x = 16

• x = -8 and x = 0

In the inequality |x| < 8, what is the range of values for x?

• x < -8

• x > 8

• x < -8 or x > 8

• -8 < x < 8

What happens to the direction of an inequality when you divide both sides by a negative number?

• It becomes undefined

• It becomes an equation

• It changes direction

• It stays the same

If the absolute value equation |3x - 1| = 14 is given, what are the two resulting equations after removing the absolute value?

• 3x - 1 = 14 and 3x - 1 = -14

• 3x - 1 = 14 and -3x + 1 = 14

• 3x - 1 = 14 and -3x + 1 = -14

• 3x - 1 = 14 and 3x + 1 = 14

What is the solution to the equation |2x + 5| = 3x + 4 when x = 1?

• 7

• 1

• 3

• 0

Why is there no solution to the equation |x - 4| = -2?

• Because the variable is not isolated

• Because the equation is not balanced

• Because x cannot be negative

• Because the absolute value cannot be negative

In the inequality |x - 4|/2 < 4, what is the first step to isolate the absolute value?

• Divide both sides by 2

• Subtract 4 from both sides

• Add 4 to both sides

• Multiply both sides by 2

What is the solution to the inequality |x - 4|/2 < 4?

• x < 12 and x > -4

• x < 8 and x > -8

• x < 12 and x > -12

• x < 12 and x > -4

When graphing the solution to the inequality |x - 4|/2 < 4, what type of dots are used on the number line?

• Dashed dots

• Open dots

• Solid dots

• Closed dots