Solving Linear Equations and Reciprocals

The video tutorial explains how to solve one-step equations by performing a single operation on both sides. It covers four examples: -6t = 24, y/5 = -8, 4/7m = -8, and -6/7r = 6. Each example demonstrates the process of isolating the variable and checking the solution through substitution. The tutorial emphasizes using reciprocals for division involving fractions.

What operation is used to solve the equation -6t = 24?

• Subtraction

• Addition

• Multiplication

• Division

What is the solution to the equation -6t = 24?

• t = 6

• t = -4

• t = 4

• t = -6

How do you isolate y in the equation y/5 = -8?

• Divide both sides by 5

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply both sides by 5

What is the solution to the equation y/5 = -8?

• y = -40

• y = 8

• y = 40

• y = -8

What is the reciprocal of 4/7 used to solve (4/7)m = -8?

• 7/4

• 4/7

• -7/4

• -4/7

What is the solution to the equation (4/7)m = -8?

• m = 14

• m = -14

• m = 8

• m = -8

What is the purpose of using the reciprocal in solving equations like (4/7)m = -8?

• To multiply fractions

• To add fractions

• To divide fractions

• To simplify the equation

What operation is used to solve the equation (-6/7)r = 6?

• Divide both sides by -7/6

• Add 6/7 to both sides

• Subtract 6/7 from both sides

• Multiply both sides by -7/6

What is the solution to the equation (-6/7)r = 6?

• r = -7

• r = 7

• r = 6

• r = -6

Why is it important to check solutions by substitution?

• To simplify the equation

• To find a new solution

• To change the equation

• To verify the solution satisfies the original equation