Inequalities using addition and subtraction | Linear inequalities | Algebra I | Khan Academy

TL;DR

This video explains the basics of solving inequalities using notation, demonstrating how to find solutions and graph them on a number line.

Transcript

what i want to do in this video is a handful of fairly simple inequality videos. But the real value of it, I think, will be just to get you warmed up in the notation of inequality. So, let's just start with one. we have x minus 5 is less than 35. So let's see if we can find all of the x's that will satisfy this equation. And that's one of the disti... Read More

Key Insights

• 🧡 Inequalities involve a range of solutions, unlike equations that typically have only one solution.
• 😫 Isolating the variable on one side of the inequality symbol is necessary to find the solution set.
• ✖️ The direction of the inequality can change when multiplying or dividing by a negative number.
• 🫥 Graphing the solution set on a number line helps visualize the range of values that satisfy the inequality.

Questions & Answers

Q: What is the difference between an equation and an inequality?

An equation typically has one solution, while an inequality has a range of solutions. Inequalities represent sets of values that satisfy a particular condition or relationship.

Q: How do you solve inequalities that involve addition or subtraction?

To solve such inequalities, isolate the variable term on one side of the inequality symbol by performing the inverse operation (i.e., adding or subtracting the same value from both sides).

Q: How do you solve inequalities with multiplication or division?

When dealing with multiplication or division, be careful if you multiply or divide by a negative number, as this will reverse the direction of the inequality.

Q: How do you graph the solution set of an inequality on a number line?

Plot the critical values (points that make the inequality true) on the number line using filled or open circles, depending on whether the inequality includes or excludes those values. Shade the region that satisfies the inequality.

Summary & Key Takeaways

• The video introduces the concept of inequalities and highlights the difference between an equation and an inequality.

• It discusses how to find solutions for inequalities by isolating the variable on one side of the inequality symbol.

• The video demonstrates how to graph the solution set on a number line by considering whether the inequality includes or excludes specific values.