Solving One-Variable Inequalities

This video tutorial introduces solving inequalities in one variable, explaining the process through examples. It covers common mistakes, special cases like no solution or infinitely many solutions, and applies these concepts to a practical problem of comparing costs from two florists. The tutorial emphasizes understanding the rules of inequalities, such as flipping the inequality sign when multiplying or dividing by a negative number, and provides guidance on graphing solutions.

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

• Combine like terms

• Distribute -4

• Add 4 to both sides

• Divide by -4

When solving -6x ≥ 12, what must you remember to do when dividing by -6?

• Subtract 6 from both sides

• Add 6 to both sides

• Keep the inequality sign the same

• Flip the inequality sign

In the inequality h ≥ -1, what type of circle should be used on the graph?

• Open circle

• Closed circle

• No circle

• Half-filled circle

What is the first step in solving the inequality 2x + 19 > -7?

• Add 19 to both sides

• Subtract 19 from both sides

• Multiply by 2

• Divide by 2

If you end up with a true statement like 15 > 9 after solving an inequality, what does it mean?

• One solution

• Infinitely many solutions

• Two solutions

• No solution

What should you do if you end up with a false statement like -5 < -6 after solving an inequality?

• Write 'infinitely many solutions'

• Solve again

• Graph the inequality

• Write 'no solution'

In the inequality 4x - 5 < 2(2x - 3), what is the first step?

• Subtract 4x from both sides

• Divide by 2

• Distribute 2

• Add 5 to both sides

When comparing costs from two florists, what inequality represents the cost from Florist A being less than Florist B?

• 4.75r + 40 ≥ 5.15r + 25

• 4.75r + 40 = 5.15r + 25

• 4.75r + 40 < 5.15r + 25

• 4.75r + 40 > 5.15r + 25

If 15 < 0.4r, what is the value of r?

• r < 37.5

• r = 37.5

• r ≤ 37.5

• r > 37.5

What should you do if you have any questions about solving inequalities?

• Try to solve it again

• Reach out for help

• Ignore the problem

• Guess the answer