Example 2: Variables on both sides | Linear equations | Algebra I | Khan Academy | Summary and Q&A

TL;DR

The video teaches how to solve equations with variables on both sides using step-by-step instructions and examples.

Key Insights

• 🍉 Separating the constant terms and variable terms makes solving equations easier.
• 🙃 Balancing equations requires performing the same operation on both sides to maintain equality.
• 🍉 Isolating the variable involves performing the opposite operation of the variable term.
• 🆘 Verifying the solution helps confirm the accuracy of the solved equation and obtained value.

Transcript

We have the equation 20 minus 7 times x is equal to 6 times x minus 6. And we need to solve for x. So the way I like to do these is we just like to separate the constant terms, which are the 20 and the negative 6 on one side of the equation. I'll put them on the right-hand side. And then we'll put all the x terms, the negative 7x and the 6x, we'll ... Read More

Questions & Answers

Q: How do you solve an equation with variables on both sides?

To solve an equation with variables on both sides, start by getting all the variable terms on one side and the constant terms on the other side. Then simplify the equation by combining like terms. Finally, isolate the variable by performing the necessary operations.

Q: Why do you need to perform the same operation on both sides of the equation?

Performing the same operation on both sides of the equation ensures that the equation remains balanced. If you add, subtract, multiply, or divide one side of the equation, you must do the same to the other side to maintain equality.

Q: How can you isolate the variable in an equation?

To isolate the variable, perform the opposite operation of the variable term. For example, if the variable is multiplied by a number, divide both sides of the equation by that number. If the variable is added or subtracted, perform the opposite operation to remove it from one side of the equation.

Q: Why is it important to verify the solution to an equation?

Verifying the solution helps ensure that the equation was solved correctly and that the solution is accurate. By substituting the obtained value back into the original equation, you can confirm if both sides of the equation remain equal.

Summary & Key Takeaways

• The video presents a step-by-step method to solve equations with variables on both sides.

• The constant terms are separated, with the constant terms on one side and the variable terms on the other side.

• The video shows how to simplify the equation by combining like terms, and then how to isolate the variable by performing necessary operations like addition, subtraction, multiplication, and division.