Solving Linear Equations and Applications

The video tutorial focuses on solving equations with variables on both sides. It explains the use of properties of equality and inverse operations to simplify and solve equations. Two examples are provided: one is a straightforward equation, and the other is an application problem involving a graphic designer's time management with new software. The tutorial emphasizes combining like terms and using opposite operations to isolate variables and find solutions.

What is the main focus of this video tutorial?

• Graphing linear equations

• Solving equations with variables on both sides

• Understanding inequalities

• Solving quadratic equations

Which operations are used to solve equations with variables on both sides?

• Addition, subtraction, multiplication, and division

• Matrix operations

• Exponentiation and logarithms

• Integration and differentiation

What is another term for inverse operations?

• Opposite operations

• Direct operations

• Complex operations

• Similar operations

In the equation 5x + 2 = 2x + 14, what are the like terms?

• 5x and 2x; 2 and 14

• 5x and 2x; 14 and 5

• 5x and 2; 2x and 14

• 5x and 14; 2x and 2

What operation is performed to eliminate 2x from the equation 5x + 2 = 2x + 14?

• Subtract 2x from both sides

• Divide both sides by 2

• Add 2x to both sides

• Multiply both sides by 2

After combining like terms in the equation 5x + 2 = 2x + 14, what is the resulting equation?

• 3x + 2 = 14

• 3x = 12

• 7x = 16

• 5x = 2x + 14

What is the final solution for the equation 5x + 2 = 2x + 14?

• x = 8

• x = 6

• x = 2

• x = 4

How do you verify the solution x = 4 for the equation 5x + 2 = 2x + 14?

• Graph the equation and check the intersection

• Substitute x = 4 back into the original equation

• Check if x = 4 satisfies a different equation

• Use a calculator to solve again

What is the left side of the equation when x = 4 is substituted back into 5x + 2?

• 22

• 20

• 18

• 24

What is the right side of the equation when x = 4 is substituted back into 2x + 14?

• 20

• 24

• 22

• 18