Exploring Absolute Value Equations and Inequalities

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

• Isolate the variable

• Add 3 to both sides

• Isolate the absolute value

• Multiply both sides by 2

When setting up the 'greater than' inequality, what should you do with the inequality sign on the left side?

• Keep it the same

• Switch it and change the sign of the number

• Multiply both sides by 2

• Add 3 to both sides

After isolating the absolute value and setting up the inequality, what is the next step?

• Add 3 to both sides

• Multiply both sides by 2

• Subtract 3 from both sides

• Divide both sides by 2

How do you represent the solution on a number line when there is no equal sign in the inequality?

• Use a dashed line

• Use an open circle

• Use a filled dot

• Use a solid line

What does the 'or' in the 'greater than' inequality indicate about the solution?

• The solution is between two numbers

• The solution is not possible

• The solution is exactly one number

• The solution is outside two numbers

What is the key difference when setting up a 'less than' inequality compared to a 'greater than' inequality?

• You switch the inequality sign

• You add 3 to both sides

• You use 'and' instead of 'or'

• You multiply both sides by 2

In a 'less than' inequality, what does the 'and' indicate about the solution?

• The solution is not possible

• The solution is exactly one number

• The solution is outside two numbers

• The solution is between two numbers

How do you solve a compound inequality?

• Multiply both sides by 2

• Combine the inequalities into one

• Ignore one part of the inequality

• Solve each part separately

When graphing a 'less than' inequality, where is the solution located on the number line?

• Outside the two numbers

• Between the two numbers

• To the right of the larger number

• To the left of the smaller number

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

• Add 3 to both sides

• Isolate the variable

• Graph the solution

• Multiply both sides by 2