Verifying and Solving Linear Equations

The video tutorial explains how to solve linear equations by isolating the variable x. It demonstrates two methods for solving the equations and verifies the solutions. The first example involves solving -8x - 24 = 4x, and the second example involves solving 2x - 28 = 6x. The tutorial emphasizes the importance of isolating the variable term and verifying the solution by substituting back into the original equation.

What is the first step in solving the equation -8x - 24 = 4x?

• Divide both sides by -8

• Multiply both sides by 4

• Subtract 24 from both sides

• Add 8x to both sides

After adding 8x to both sides of the equation -8x - 24 = 4x, what is the resulting equation?

• 0 = 12x - 24

• 12x = 24

• -24 = 12x

• x = -2

What is the alternative first step in solving the equation -8x - 24 = 4x?

• Add 24 to both sides

• Subtract 4x from both sides

• Multiply both sides by -1

• Divide both sides by 4

What is the final solution for x in the equation -8x - 24 = 4x?

• x = 0

• x = 2

• x = 4

• x = -2

How do you verify that x = -2 is a solution to the equation -8x - 24 = 4x?

• By solving the equation again

• By using a calculator

• By substituting x = -2 into the equation and checking if both sides are equal

• By graphing the equation

What is the first step in solving the equation 2x - 28 = 6x?

• Add 28 to both sides

• Multiply both sides by 6

• Subtract 2x from both sides

• Divide both sides by 2

After subtracting 2x from both sides of the equation 2x - 28 = 6x, what is the resulting equation?

• -28 = 4x

• 0 = 4x - 28

• 4x = 28

• x = -7

What is the final solution for x in the equation 2x - 28 = 6x?

• x = 14

• x = -7

• x = 7

• x = 0

How do you verify that x = -7 is a solution to the equation 2x - 28 = 6x?

• By graphing the equation

• By solving the equation again

• By substituting x = -7 into the equation and checking if both sides are equal

• By using a calculator

What is the purpose of verifying a solution to an equation?

• To ensure the solution satisfies the original equation

• To find a different solution

• To check for calculation errors

• To simplify the equation further