Solving Linear Equations and Properties

The video tutorial explains how to solve linear equations by removing parentheses using the distributive property. It begins with an introduction to the concept, followed by a review of the distributive property with examples. The tutorial then provides step-by-step solutions to two example equations, demonstrating the use of the distributive and subtraction properties of equality. The video concludes by reinforcing the learned concepts and verifying solutions by substituting them back into the original equations.

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

• To add like terms

• To change the order of operations

• To solve quadratic equations

• To simplify expressions by removing parentheses

Which property allows you to reorder terms in an expression?

• Subtraction Property

• Commutative Property

• Associative Property

• Distributive Property

How do you apply the distributive property to the expression 2(x + 1)?

• 2x + 1x

• x + 2

• 2x + 2

• 2x + 1

What is the first step in solving the equation 5(x + 2) = 27?

• Divide both sides by 5

• Subtract 2 from both sides

• Add 10 to both sides

• Distribute 5 across (x + 2)

After distributing in the equation 5(x + 2) = 27, what is the resulting equation?

• 5x + 2 = 27

• 5x + 10 = 27

• 5x + 2 = 17

• 5x + 10 = 17

What is the solution for x in the equation 5(x + 2) = 27?

• x = 5

• x = 3.4

• x = 17/5

• x = 7

In the equation (-3/7)(x - 2) = -18, what is the first step to solve for x?

• Add 2 to both sides

• Multiply both sides by -7/3

• Distribute -3/7 across (x - 2)

• Subtract 6/7 from both sides

What is the reciprocal of -3/7?

• 3/7

• -7/3

• 7/3

• -3/7

What is the solution for x in the equation (-3/7)(x - 2) = -18?

• x = 18

• x = 42

• x = 44

• x = 132/3

What is the key takeaway from this lesson on solving linear equations?

• Equations can only be solved using the subtraction property

• The distributive property is essential for removing parentheses

• Linear equations cannot be solved without a calculator

• The associative property is used to solve all equations