M3 Solving Equations with variables on both sides

Front

What is an equation?

Back

An equation is a mathematical statement that asserts the equality of two expressions, typically containing variables.

Front

What does it mean to solve an equation?

Back

To solve an equation means to find the value(s) of the variable(s) that make the equation true.

Front

What are like terms?

Back

Like terms are terms that have the same variable raised to the same power, allowing them to be combined.

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 parenthesis.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable alone on one side of the equation.

Front

What is the first step in solving 8 - 3a + 12 = 2a?

Back

Combine like terms on the left side to simplify the equation.

Front

What does it mean if an equation has no solution?

Back

An equation has no solution if there are no values for the variable that can satisfy the equation.

Front

What does it mean if an equation has all real numbers as a solution?

Back

It means that any value for the variable will satisfy the equation, indicating that the two sides are equivalent for all values.

Front

What is the first step in solving 3x + 6 = 10 + 3x + 4x?

Back

Combine like terms 3x and 4x on the same side of the equation.

Front

How do you check if your solution to an equation is correct?

Back

You substitute the solution back into the original equation to see if both sides are equal.