Solving Equations with Variables on Both Sides

This video tutorial introduces solving equations with variables on both sides, a new skill in Math 8. It covers verifying solutions, using properties of equality, and isolating variables. Exercises are provided to practice these concepts, including using the symmetric property. The lesson emphasizes the importance of maintaining balance in equations by performing the same operations on both sides.

What is the fundamental idea behind a solution to an equation?

• A value that makes the equation false

• A value that balances both sides of the equation

• A value that only works for linear equations

• A value that requires complex numbers

What does the addition property of equality allow you to do?

• Add different values to each side of the equation

• Subtract the same value from both sides of the equation

• Multiply both sides of the equation by the same number

• Add the same value to both sides of the equation

Which property of equality is used when dividing both sides of an equation by the same number?

• Addition property of equality

• Subtraction property of equality

• Division property of equality

• Multiplication property of equality

What does it mean to isolate a variable in an equation?

• To multiply the variable by zero

• To remove the variable from the equation

• To get the variable by itself on one side of the equation

• To divide the variable by itself

What is the result of applying the subtraction property of equality to both sides of an equation?

• The equation becomes an inequality

• The equation automatically solves itself

• The equation remains true

• The equation becomes undefined

What is the division property of equality primarily used for in solving equations?

• To eliminate fractions from the equation

• To simplify the equation's constants

• To isolate the variable

• To convert the equation into a quadratic form

In the equation 5x + 6 = 2x + 30, what is the first step to isolate the variable?

• Subtract 2x from both sides

• Add 2x to both sides

• Add 6 to both sides

• Subtract 6 from both sides

What is the solution to the equation 3x = 24?

• x = 7

• x = 12

• x = 9

• x = 8

In the equation 7n + 5 = 2n + 25, what is the value of n?

• n = 5

• n = 4

• n = 6

• n = 7

Why might flipping an equation make it easier to solve?

• It always results in a simpler equation

• It automatically solves the equation

• It ensures the variable has a positive coefficient

• It changes the equation into a linear form