Quadratic inequality example 2 | Functions and their graphs | Algebra II | Khan Academy

TL;DR

This video explains how to simplify and graph an inequality expression on a number line.

Transcript

We've got the inequality negative x times the expression 2x minus 14 is greater than or equal to 24. So I encar, encourage you to pause this video now and think about what the solution set to this inequality would actually be, and actually plot the solution set on a number line. So I'm assuming you've given a go at it, so let's just try to simplify... Read More

Key Insights

• 😑 Inequalities involving quadratic expressions can be simplified by factoring and analyzing the signs of the factors.
• 🫥 The solution set for an inequality on a number line represents the range of values that satisfy the inequality.
• 😑 The signs of the factors in a quadratic expression help determine whether the inequality is ≤ or ≥.

Questions & Answers

Q: How is the inequality -x(2x-14) ≥ 24 simplified?

The inequality is distributed and simplified to become x² - 7x + 12 ≥ 0.

Q: How is the quadratic expression x² - 7x + 12 factored?

The quadratic expression is factored as (x-3)(x-4) ≤ 0, considering two numbers whose sum is -7 and product is 12.

Q: What does it mean for an expression to be ≤ 0?

An expression being ≤ 0 means that either one or both of its factors are 0 or they have different signs.

Q: What is the solution set for the inequality x² - 7x + 12 ≤ 0?

The solution set is x ≤ 3 and x ≥ 4, which represents values less than or equal to 3 and greater than or equal to 4.

Summary & Key Takeaways

• The video simplifies the inequality -x(2x-14) ≥ 24 and converts it to x² - 7x + 12 ≤ 0.

• By factoring the quadratic expression, x² - 7x + 12, it becomes (x-3)(x-4) ≤ 0.

• The solution set for the inequality is x ≤ 3 and x ≥ 4, which is graphically represented on a number line.