Solving Basic Linear Equations

This video tutorial covers the basics of solving linear equations, a fundamental concept in algebra. It provides two examples: solving 2x - 18 = 14 and 4y + 22 = 0. The instructor explains the step-by-step process of isolating the variable by moving terms across the equation and using inverse operations like addition, subtraction, and division. The video emphasizes the importance of having a systematic approach to solving equations, especially when dealing with more complex problems. It concludes with a brief mention of more advanced topics to be covered in future videos.

Why are linear equations considered fundamental in various math classes?

• They are the simplest type of equations.

• They are easy to solve.

• They appear frequently in different areas of mathematics.

• They are the only type of equations used in algebra.

What is the first step in solving the equation 2x - 18 = 14?

• Add 18 to both sides.

• Subtract 18 from both sides.

• Multiply both sides by 2.

• Divide both sides by 2.

After adding 18 to both sides of the equation 2x - 18 = 14, what is the resulting equation?

• 2x = -4

• 2x = 32

• x = 16

• x = 32

What operation is used to isolate x in the equation 2x = 32?

• Division

• Multiplication

• Subtraction

• Addition

What is the solution to the equation 2x - 18 = 14?

• x = 32

• x = 14

• x = 18

• x = 16

What is the first step in solving the equation 4y + 22 = 0?

• Multiply both sides by 4.

• Subtract 22 from both sides.

• Add 22 to both sides.

• Divide both sides by 4.

After subtracting 22 from both sides of the equation 4y + 22 = 0, what is the resulting equation?

• y = 22

• 4y = 22

• 4y = -22

• y = -22

What operation is used to isolate y in the equation 4y = -22?

• Multiplication

• Subtraction

• Division

• Addition

What is the reduced fraction form of the solution to the equation 4y + 22 = 0?

• y = -5 and 1/2

• y = -22/4

• y = -5.5

• y = -11/2

What is the basic idea for solving linear equations as mentioned in the video?

• Guess the value of the variable.

• Put all variables on one side and all numbers on the other.

• Use a calculator for all steps.

• Always convert the solution to a decimal.