Determining Solutions of Simplified Equations

This video tutorial teaches how to determine the number of solutions an equation has by transforming it into a simpler form. It reviews patterns for identifying solutions based on variable terms and constants. The tutorial explains simplifying and transforming equations, predicting solutions, and provides examples to illustrate different solution patterns. It concludes with understanding infinite solutions and true equations.

What is the main goal of this lesson?

• To learn about different types of equations

• To solve complex equations

• To memorize mathematical formulas

• To determine the number of solutions an equation has

If the variable term is only on one side of the equation, how many solutions does it have?

• Two solutions

• Infinite solutions

• One solution

• No solutions

What does it mean if the variable terms are equal but the constants are not?

• The equation has no solutions

• The equation has one solution

• The equation is invalid

• The equation has infinite solutions

What is the result of simplifying an equation by distributing and combining like terms?

• A new version of the same equation

• A more complex equation

• A different equation

• An invalid equation

In the example where the variable terms are the same but the constants are different, what is the number of solutions?

• Infinite solutions

• Two solutions

• One solution

• No solutions

What does it indicate if you end up with a false equation like 12 equals 3?

• The equation is invalid

• The equation has no solutions

• The equation has infinite solutions

• The equation has one solution

What should you do if the variable terms are not equal and you don't recognize the pattern?

• Guess the number of solutions

• Transform or simplify the equation

• Leave the equation as it is

• Change the constants

What does it mean if you end up with a variable equal to a constant after transforming an equation?

• The equation has one solution

• The equation has infinite solutions

• The equation is invalid

• The equation has no solutions

In the example where the variable terms and constants are the same on both sides, what is the number of solutions?

• No solutions

• Two solutions

• Infinite solutions

• One solution

What does it indicate if you end up with a true equation like 87 equals 87?

• The equation has one solution

• The equation has no solutions

• The equation is invalid

• The equation has infinite solutions