Solving Absolute Value Equations and Inequalities

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

• Multiplying both sides by a constant

• Adding a constant to both sides

• Writing two separate inequalities

• Graphing the inequality

When graphing the solution of an absolute value inequality on a number line, what does an open circle represent?

• The value is a boundary point

• The value is not included in the solution

• The value is a midpoint

• The value is included in the solution

How do you handle fractions when solving absolute value inequalities?

• Add the fractions to both sides

• Multiply by the least common multiple of the denominators

• Divide by the largest denominator

• Subtract the fractions from both sides

What is the interval notation for the solution of an inequality where x is greater than 63/8?

• (-63/8, ∞)

• (-∞, 63/8)

• (63/8, ∞)

• (-∞, -63/8)

Tags

CCSS.6.EE.B.8

What should you do first when there are numbers outside the absolute value expression?

• Subtract the numbers from both sides

• Add the numbers to both sides

• Isolate the absolute value expression

• Multiply both sides by the numbers

What happens to the direction of the inequality when you multiply or divide by a negative number?

• It becomes an equality

• It changes direction

• It remains the same

• It becomes undefined

Tags

CCSS.6.EE.B.8

Why is the solution to an absolute value inequality always true when the inequality is greater than a negative number?

• Because absolute values are always positive or zero

• Because negative numbers are not allowed

• Because the inequality is always false

• Because the absolute value can be negative

What is the solution to an absolute value inequality that is less than or equal to a negative number?

• No solution

• Only positive numbers

• Only negative numbers

• All real numbers

What should you be cautious of when dealing with absolute value inequalities?

• Inequalities that have no solution

• Inequalities that involve fractions

• Inequalities that are less than or equal to a negative number

• Inequalities that are greater than a positive number

What is the interval notation for a solution that includes all real numbers?

• (-∞, -∞)

• (0, ∞)

• (-∞, ∞)

• (-∞, 0)

Tags

CCSS.6.EE.B.8