Solving Multistep Equations with Variables on Both Sides

This video tutorial focuses on solving multi-step equations, particularly those with variables on both sides of the equal sign. It provides examples and step-by-step instructions on how to simplify and solve these equations using techniques like combining like terms and applying the inverse operation. The tutorial also covers the use of the distributive property and offers a challenge problem to reinforce learning. Throughout, the importance of checking solutions is emphasized.

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

• Combine like terms on the same side

• Move all variables to one side using inverse operations

• Distribute values inside parentheses

• Subtract constants from both sides

What operation is used to move a positive term across the equal sign?

• Division

• Multiplication

• Subtraction

• Addition

When combining 10x and -4x on the same side, what is the result?

• 14x

• 6x

• -6x

• -14x

What should you do if there are no like terms or parentheses on a side of the equation?

• Nothing, as it is already simplified

• Check for possible distribution

• Start combining opposite sides

• Move to the other side immediately

How do you handle a negative term when distributing across parentheses?

• Convert it to a positive

• Add it instead of multiplying

• Multiply as is

• Ignore the negative sign

What is the result of combining -7x and -5x?

• -2x

• 2x

• 12x

• -12x

What is the correct operation to isolate a variable when it appears on both sides of the equation?

• Multiplication

• Subtraction

• Addition

• Either addition or subtraction, depending on the terms

After distributing and combining like terms, what is the next step?

• Isolate the variable

• Simplify the constants

• Combine opposite sides

• Check the solution

What does a negative divided by a negative yield when solving for x?

• A positive number

• A negative number

• Undefined

• Zero

In the final example, what is the value of x when the equation involves decimals?

• 23.5

• 21.5

• 22.5

• 20.5