Solving Linear Equations and Operations

The video tutorial explains how to solve a linear equation in one variable by isolating the variable, distributing terms, and simplifying the equation. It demonstrates the process of solving the equation -4(3x - 2) = 42, including distributing the negative 4, isolating the variable term, and solving for x. The solution is simplified to x = -17/6, and the tutorial verifies the solution by substituting it back into the original equation to ensure it holds true. The video emphasizes understanding the steps involved in solving and checking linear equations.

What is the first step in solving a linear equation?

• Add a constant to both sides

• Isolate the variable on one side

• Divide by the coefficient of the variable

• Multiply both sides by zero

What operation is used to clear the parentheses in the equation -4(3x - 2) = 42?

• Division

• Distribution

• Subtraction

• Addition

How do you treat subtraction when distributing a negative number?

• As a fraction

• As a positive number

• As a negative number

• As zero

What is the result of subtracting 8 from both sides of the equation -12x + 8 = 42?

• -12x = 30

• -12x = 42

• -12x = 34

• -12x = 50

What operation is used to solve for x in the equation -12x = 34?

• Division

• Addition

• Multiplication

• Subtraction

What is the simplified form of the fraction -34/12?

• -34/6

• -17/6

• -34/24

• -17/12

What is the purpose of substituting the solution back into the original equation?

• To find a new solution

• To verify the solution is correct

• To change the equation

• To simplify the equation

What is the result of the multiplication -4 * -21/2?

• 21

• -21

• -42

• 42

What is the common denominator used when subtracting -17/2 and 2?

• 6

• 1

• 2

• 4

What does the equation 42 = 42 indicate after verification?

• The solution is incorrect

• The equation needs more steps

• The solution is correct

• The equation is unsolvable