Solving Linear Equations and Operations

The video tutorial explains how to solve linear equations by isolating the variable. It provides four examples, each demonstrating the process of performing inverse operations to both sides of the equation to maintain equality. Each solution is verified by substituting the found value back into the original equation to ensure correctness. The tutorial emphasizes the importance of maintaining balance in equations and provides a clear, step-by-step approach to solving them.

What is the first step in solving an equation to find the value of a variable?

• Add the same number to both sides

• Divide both sides by the variable

• Isolate the variable on one side

• Multiply both sides by zero

In the equation m - 6 = -3, what operation is needed to isolate m?

• Multiply both sides by 6

• Add 6 to both sides

• Divide both sides by 6

• Subtract 6 from both sides

After solving m - 6 = -3, what is the value of m?

• m = 6

• m = 3

• m = 0

• m = -3

In the equation 8 = p + 12, what operation is needed to isolate p?

• Subtract 12 from both sides

• Add 12 to both sides

• Divide both sides by 12

• Multiply both sides by 12

What is the solution to the equation 8 = p + 12?

• p = 8

• p = 12

• p = 4

• p = -4

In the equation 3 + w = 9, what operation is needed to isolate w?

• Divide both sides by 3

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by 3

What is the solution to the equation 3 + w = 9?

• w = 6

• w = 12

• w = 9

• w = 3

In the equation -2 = x - 7, what operation is needed to isolate x?

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply both sides by 7

• Divide both sides by 7

What is the solution to the equation -2 = x - 7?

• x = -5

• x = 0

• x = 5

• x = 7

Why is it important to perform the same operation on both sides of an equation?

• To simplify the equation

• To change the variable

• To maintain the equality

• To make the equation more complex