Exploring Variables on Both Sides in Equations

This video tutorial covers solving multi-step equations with variables on both sides. It begins with an introduction to the concept, followed by detailed steps on using the distributive property, handling negative coefficients, and solving equations that result in fractional solutions. The tutorial emphasizes combining like terms and isolating variables to find solutions.

What property is used first when solving equations with parentheses?

• Additive property

• Distributive property

• Associative property

• Commutative property

After distributing and combining like terms, what is the next step in solving for the variable?

• Add the constants

• Multiply by the variable's coefficient

• Subtract the smaller variable term from the larger one

• Divide by the coefficient of the variable

What is the result of solving the equation 5v - 30 = 2v + 18 for v?

• v = 16

• v = 12

• v = 24

• v = 8

In the second problem, what is the result of distributing -3 to 8y and -12?

• 24y + 36

• -24y - 36

• 24y - 36

• -24y + 36

How do you isolate the variable y in the equation -22y + 36 = 300?

• Subtract 36 from both sides

• Add 36 to both sides

• Multiply both sides by -22

• Divide both sides by -22

What is the value of y after solving -22y + 36 = 300?

• y = 14

• y = -12

• y = -14

• y = 12

What operation is necessary to simplify the equation 9(x + 1/2) = 3(x + 11)?

• Addition

• Division

• Subtraction

• Multiplication

After simplifying and distributing, what is the simplified form of the equation 9(x + 1/2) = 3(x + 11)?

• 9x + 1 = 3x + 33

• 9x + 1 = 6x + 22

• 9x + 0.5 = 3x + 11

• 18x + 2 = 6x + 22

What is the final value of x in the equation 9x + 1 = 6x + 22?

• x = 11/3

• x = 21

• x = 7

• x = 3

How do you isolate x in the equation 3x + 1 = 22?

• Add 1 to both sides

• Subtract 1 from both sides

• Divide both sides by 3

• Multiply both sides by 3