Multi-Step with Special Solutions

Front

What does it mean when an equation has 'no solution'?

Back

An equation has 'no solution' when there are no values for the variable that can satisfy the equation, often resulting in a contradiction.

Front

What is a special solution in the context of equations?

Back

A special solution refers to specific values or conditions under which an equation holds true, such as identities or contradictions.

Front

How do you determine if an equation has no solution?

Back

To determine if an equation has no solution, simplify both sides and check for contradictions, such as a statement like '0 = 5'.

Front

What is the first step in solving a multi-step equation?

Back

The first step is to simplify both sides of the equation, which may involve distributing, combining like terms, or isolating the variable.

Front

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

Back

Isolating a variable means rearranging the equation so that the variable is on one side and all other terms are on the opposite side.

Front

What is the significance of the distributive property in solving equations?

Back

The distributive property allows you to multiply a single term by each term inside a parenthesis, which is essential for simplifying expressions in equations.

Front

What is the solution to the equation 2(x + 5) = 2x + 5?

Back

The solution is 'no solution' because both sides simplify to the same expression, leading to a contradiction.

Front

What does it mean when two expressions are equivalent?

Back

Two expressions are equivalent if they yield the same value for all values of the variable.

Front

How can you check your solution to an equation?

Back

You can check your solution by substituting the value back into the original equation to see if both sides are equal.

Front

What is the role of combining like terms in solving equations?

Back

Combining like terms simplifies the equation, making it easier to isolate the variable and find the solution.