Types of Solutions

Front

What is a solution in the context of algebraic equations?

Back

A solution is a value or set of values that satisfy an equation, making it true when substituted into the equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What is the first step in solving the equation 1 + 8x + 9 = -20 + 2x?

Back

Combine like terms on both sides of the equation.

Front

What does it mean to combine like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

What is the solution to the equation -1 + 2x = 6x + 11?

Back

The solution is x = -3.

Front

What is the process of checking your solution in an equation?

Back

To check your solution, substitute the value back into the original equation to see if both sides are equal.

Front

What is the significance of the equal sign in an equation?

Back

The equal sign indicates that the expressions on both sides of it have the same value.

Front

What is the method to solve the equation 5 - 6x = 17 - 8x?

Back

Add 8x to both sides and then isolate x by performing inverse operations.

Front

What does it mean for an equation to be balanced?

Back

An equation is balanced when both sides have the same value, meaning any operation performed on one side must also be performed on the other.

Front

What is the importance of understanding the properties of equality?

Back

The properties of equality allow you to manipulate equations while maintaining their truth value.