Solving Equations with Variables on Both Sides

Mrs. Yaud teaches students how to solve algebraic equations with variables on both sides. The lesson covers steps for solving such equations, including using the distributive property, simplifying both sides, and isolating variables. Example problems are solved to illustrate these steps, and special cases like no solution or infinitely many solutions are discussed. The lesson concludes with a problem involving the surface area and volume of a rectangular prism.

What is the first step in solving equations with variables on both sides?

• Move constants to one side

• Use the distributive property to eliminate parentheses

• Isolate the variable

• Combine like terms

When simplifying the equation, what should you do after distributing?

• Isolate the variable immediately

• Combine like terms and simplify each side

• None of the above

• Check the solution

In the example problem, what is the value of 'z' when solved?

• 1

• 2

• 0

• -1

What is the correct operation to move terms in an equation?

• Multiplication only

• Either addition or subtraction, depending on the term

• Subtraction only

• Addition only

How do you verify a solution in an equation?

• Ask a friend

• Solve the equation again

• Substitute the solution back into the original equation

• Guess and check

What is the first step when you encounter parentheses in an equation?

• Isolate the variable

• Simplify the constants

• Use the distributive property

• Combine like terms

What indicates an equation has no solution?

• When the variables cancel out and a false statement remains

• When the variables do not cancel out

• When any number can be a solution

• When the equation simplifies to a true statement

What does it mean if an equation simplifies to a true statement like '24 = 24'?

• The equation is incorrect

• Infinitely many solutions

• One unique solution

• No solution

In the context of a rectangular prism, if the surface area equals the volume, what could be a possible value of 'x'?

• 6

• 24

• 12

• 18

When solving for 'x' in equations involving a rectangular prism's surface area and volume, what mathematical operation is typically used?

• Multiplication

• Subtraction

• Division

• Addition