Solving Linear Equations and Inequalities

The video tutorial explains how to solve the equation 3(x - 8) - 6 = 5(x + 6) by isolating the variable x. It involves distributing terms, simplifying both sides, and using inverse operations to solve for x. The solution is verified by substituting the value back into the original equation, confirming that x = -30 satisfies the equation.

What is the primary goal when solving the equation 3(x - 8) - 6 = 5(x + 6)?

• To find the value of y

• To find the value of x that makes both sides equal

• To simplify the equation as much as possible

• To eliminate all numbers from the equation

What is the result of distributing 3 on the left side of the equation 3(x - 8) - 6?

• 3x - 8 - 6

• 3x + 24 - 6

• 3x - 24 - 6

• 3x + 8 - 6

After distributing and simplifying, what does the left side of the equation become?

• 5x + 30

• 3x - 30

• 5x - 30

• 3x + 30

What operation is performed to eliminate the 5x on the right side of the equation?

• Divide both sides by 5

• Multiply both sides by 5

• Add 5x to both sides

• Subtract 5x from both sides

What is the equation after subtracting 5x from both sides?

• -2x - 30 = 30

• 2x - 30 = 30

• 2x + 30 = 30

• -2x + 30 = 30

What is the next step after obtaining the equation -2x - 30 = 30?

• Subtract 30 from both sides

• Add 30 to both sides

• Multiply both sides by 2

• Divide both sides by 2

What is the equation after adding 30 to both sides?

• -2x = 60

• 2x = 60

• -2x = 30

• 2x = 30

What operation is used to solve for x in the equation -2x = 60?

• Divide both sides by -2

• Multiply both sides by -2

• Add 2 to both sides

• Subtract 2 from both sides

What is the value of x after solving the equation -2x = 60?

• 30

• -30

• 60

• -60

How can you verify that x = -30 is the correct solution?

• Check if x = -30 satisfies a different equation

• Add 30 to x = -30 and see if it equals 0

• Substitute x = -30 back into the original equation and check both sides

• Multiply x = -30 by 2 and see if it equals 60