Solving Linear Equations and Operations

This video tutorial covers solving one-step equations using multiplication and division. It explains what constitutes a solution to an equation and provides examples to illustrate the concept. The tutorial also discusses equality principles and demonstrates how to isolate variables to solve equations. Finally, it applies these techniques to a real-world problem involving the cost of gasoline.

What is a solution to an equation?

• A value that makes the equation true

• A value that makes the equation false

• Any number that can be substituted for a variable

• Any random number

If x = 3 is a solution to 6x = 18, what operation verifies this?

• Division

• Subtraction

• Addition

• Multiplication

How do you check if x = 9 is a solution for 8x = 72?

• Add 9 to both sides of the equation

• Substitute 9 for x and check if 8 * 9 equals 72

• Subtract 9 from both sides of the equation

• Divide both sides by 9

What happens if you divide both sides of an equation by zero?

• The equation becomes false

• The equation remains true

• The operation is undefined

• The equation is solved

What is the goal when solving linear equations?

• To add variables to both sides

• To isolate the variable on one side

• To multiply both sides by zero

• To make both sides equal zero

How do you solve 3x = 36 for x?

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 3

• Divide both sides by 3

What operation would you use to solve y/2 = 18?

• Multiply both sides by 2

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by 2

In the equation 56 = 7x, what is the value of x?

• 7

• 8

• 9

• 10

How do you solve y/6 = 15 for y?

• Divide both sides by 6

• Multiply both sides by 6

• Subtract 6 from both sides

• Add 6 to both sides

If gasoline costs $3 per gallon and you spend $42, how many gallons did you buy?

• 13 gallons

• 14 gallons

• 15 gallons

• 12 gallons