Solving equations with variables on both sides

Front

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

Back

The first step is to simplify both sides of the equation, if necessary, and then move all variable terms to one side and constant terms to the other side.

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 does it mean to combine like terms in an equation?

Back

Combining like terms means to add or subtract terms that have the same variable raised to the same power.

Front

What is the distributive property and how is it used in solving equations?

Back

The distributive property states that a(b + c) = ab + ac. It is used to eliminate parentheses in equations by distributing the multiplier across the terms inside the parentheses.

Front

What is the solution to an equation?

Back

The solution to an equation is the value of the variable that makes the equation true.

Front

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

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 a linear equation?

Back

A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants and x is the variable.

Front

What does it mean for an equation to have no solution?

Back

An equation has no solution when the variable cancels out and results in a false statement, such as 0 = 5.

Front

What does it mean for an equation to have infinitely many solutions?

Back

An equation has infinitely many solutions when the variable cancels out and results in a true statement, such as 0 = 0.

Front

What is the importance of maintaining balance when solving equations?

Back

Maintaining balance means that whatever operation you perform on one side of the equation must also be performed on the other side to keep the equation true.