Solving Linear Equations and Proportions

The video tutorial explains how to identify and solve linear equations that may not appear linear at first glance. It introduces the concept of proportions and demonstrates solving these equations using cross multiplication and the distributive property. The tutorial includes examples and checks the solutions for accuracy, ensuring a comprehensive understanding of the process.

What is the first step in solving a proportion like x/5 = 6/12?

• Divide both sides by 2

• Cross multiply

• Add the fractions

• Subtract the fractions

When solving the equation 2(x + 1/3) = 4(x - 1), what property is used?

• Identity Property

• Commutative Property

• Distributive Property

• Associative Property

What is the solution to the equation 2x + 2/3 = 4x - 4?

• x = 3/14

• x = 14/3

• x = 3/7

• x = 7/3

How do you verify the solution to a linear equation?

• By using a calculator

• By solving a different equation

• By substituting the solution back into the original equation

• By graphing the equation

What is the result of cross-multiplying 4/3 = 8/3?

• 12 = 12

• 4 = 4

• 8 = 8

• 16 = 16

What is the first step in solving the equation 6 + x = 3(7x + 2/3)?

• Subtract x from both sides

• Divide by 3

• Distribute the 3

• Add 6 to both sides

What is the solution to the equation 48 + 8x = 21x + 2?

• x = 46/13

• x = 13/46

• x = 23/13

• x = 13/23

How do you verify the solution to the equation 6 + x = 3(7x + 2/3)?

• By graphing the equation

• By using a calculator

• By solving a different equation

• By checking if both sides are equal when x is substituted

What is the common denominator used in the verification of the second example?

• 3

• 8

• 13

• 39

What is the final check for the solution of the second example?

• Cross-multiplying the fractions

• Adding the fractions

• Dividing the fractions

• Subtracting the fractions