Types of Solutions 1

Front

What is a solution in the context of equations?

Back

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

Front

What does it mean if an equation has no solution?

Back

It means there are no values that can be substituted into the equation to make it true.

Front

What does it mean if an equation has one solution?

Back

It means there is exactly one value that satisfies the equation.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means there are countless values that satisfy the equation, often due to variables being equal.

Front

What is the first step in solving the equation -2(2x - 4) = 3x - 7?

Back

Distribute the -2 to both terms inside the parentheses.

Front

How do you combine like terms in an equation?

Back

You add or subtract coefficients of the same variable to simplify the equation.

Front

What is the purpose of moving variables to one side of an equation?

Back

To isolate the variable and make it easier to solve for its value.

Front

What is the purpose of moving constants to one side of an equation?

Back

To simplify the equation and help isolate the variable.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by each term inside a parentheses.

Front

What is an example of an equation with no solution?

Back

An example is 2x + 3 = 2x - 5, which simplifies to 3 = -5.