Solving One-Variable Inequalities

What are the symbols used to represent inequalities?

• Equal to, not equal to, less than, greater than

• Equal to, less than, greater than, approximately equal to

• Less than, greater than, less than or equal to, greater than or equal to

• Plus, minus, multiply, divide

When should you flip the inequality sign?

• When multiplying or dividing both sides by a negative number

• When multiplying or dividing both sides by a positive number

• When subtracting a positive number from both sides

• When adding a positive number to both sides

What is the first step in solving the inequality -4(3x - 1) + 6x ≥ 16?

• Subtract 4 from both sides

• Distribute the -4 through the parentheses

• Divide both sides by -6

• Combine like terms

After distributing and combining like terms, what is the next step in solving -4(3x - 1) + 6x ≥ 16?

• Add 4 to both sides

• Subtract 4 from both sides

• Divide both sides by -6

• Multiply both sides by -6

In the inequality -6x ≥ 12, what is the solution for x?

• x ≤ -2

• x ≥ -2

• x ≤ 2

• x ≥ 2

How do you graph the solution x ≤ -2 on a number line?

• Filled circle at -2, shading to the left

• Filled circle at -2, shading to the right

• Open circle at -2, shading to the left

• Open circle at -2, shading to the right

What is the solution to the inequality 8 - 2x > 1?

• x < 3.5

• x > 3.5

• x < -3.5

• x > -3.5

What does it mean if the variables cancel out and the resulting statement is true (e.g., 15 > 9)?

• There are infinitely many solutions

• There are no solutions

• There is one unique solution

• The solution is undefined

What does it mean if the variables cancel out and the resulting statement is false (e.g., -5 < -6)?

• There are no solutions

• There are infinitely many solutions

• There is one unique solution

• The solution is undefined

For what number of roses is florist A cheaper than florist B?

• Less than 37 roses

• More than 37 roses

• More than 38 roses

• Less than 38 roses