1 solution, no solution, infinitely many solutions (for linear equations)

TL;DR

This video explains the different types of linear equations and their solutions, including equations with no solution and equations with infinitely many solutions.

Transcript

in this video I'm going to show you guys three linear equations and you'll see the difference between all these threes and they have different response pay attention to the special the more strange cases and you see all the left hand side are actually the same I make it on purpose anyways let's look at the first one we have -3 * the parenthesis 2x ... Read More

Key Insights

• #️⃣ Distributing a number into parentheses is an important step in solving linear equations.
• #️⃣ Moving variables and numbers from one side of the equation to the other ensures consistency in the equation.
• ❓ Equations with no solution result in a false statement, while equations with infinitely many solutions result in a true statement.

Questions & Answers

Q: What should be the first step when solving an equation with a parentheses?

The first step is to distribute the number in front of the parentheses into the terms inside the parentheses. This is done when there are no powers involved.

Q: How do you move variables and numbers from one side of the equation to the other?

To move variables from one side of the equation to the other, use the opposite operation (addition or subtraction) to cancel out the term. The same process is applied to move numbers from one side to the other.

Q: What is the solution for an equation with no solution?

An equation with no solution means that the statement in the equation is false. In this case, there is no value that solves the equation.

Q: How do you know if an equation has infinitely many solutions?

If, after simplifying the equation, you end up with a true statement (e.g., 0 = 0), it means that the equation has infinitely many solutions. Any real number can be the solution in this case.

Summary & Key Takeaways

• The video presents three linear equations and discusses the steps to solve them.

• The first equation is solved by distributing a number into the parentheses and then collecting like terms.

• The second equation has no solution because it results in a false statement.

• The third equation has infinitely many solutions, meaning that any real number can be the solution.