Solving Equations with Variables

This video tutorial covers solving equations with variables on each side, including handling grouping symbols and fractions. It provides step-by-step examples and emphasizes techniques like cross multiplication and using the distributive property. The tutorial concludes with tips for ensuring accuracy in solving equations.

What is the main objective of this lesson?

• To solve equations with variables on one side

• To solve quadratic equations

• To solve equations with variables on both sides

• To solve linear equations

In Example 1, what is the first step to solve the equation 5y - 8 = 3y + 12?

• Subtract 3y from both sides

• Multiply both sides by 2

• Add 8 to both sides

• Divide both sides by 5

What happens if the variables cancel out completely in an equation?

• The solution is all real numbers

• The equation is false

• The equation is always true

• The equation has no solution

In Example 2, what is the first step to solve the equation 11 - 3y = 8y + 1?

• Add 1 to both sides

• Subtract 8y from both sides

• Add 3y to both sides

• Subtract 11 from both sides

What is the purpose of using the distributive property in solving equations?

• To move variables to one side

• To simplify the equation

• To eliminate fractions

• To combine like terms

In Example 3, what indicates that an equation has no solution?

• The variables are equal

• The constants are equal

• The equation results in a false statement

• The equation results in a true statement

How do you handle fractions in equations according to Example 4?

• Add the fractions

• Divide both sides by the highest common denominator

• Subtract the fractions

• Multiply both sides by the lowest common denominator

In Example 5, what is the result when the equation 18 - 4K = -10 - 4K is solved?

• K = 0

• K = 1

• All real numbers

• No solution

What is the first step in solving equations with grouping symbols as shown in Example 6?

• Combine like terms

• Use the distributive property

• Subtract all terms

• Add all terms

In Example 7, what method is used to solve equations with fractions?

• Subtraction

• Addition

• Division

• Cross-multiplication