Solving multi-step problems using linear equations in one variable

Front

What is a linear equation in one variable?

Back

Front

What does it mean if an equation has no solution?

Back

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

Front

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

Back

An equation has infinitely many solutions when any value for the variable satisfies the equation, often resulting in a true statement.

Front

Back

This equation has no solutions because simplifying both sides leads to a contradiction (7 = -2).

Front

How do you determine if an equation has one solution?

Back

An equation has one solution if, after simplifying, you can isolate the variable to find a specific value.

Front

Back

This equation has no solution because simplifying leads to a contradiction (-3 = 3).

Front

Back

Front

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

Back

The first step is to simplify both sides of the equation, if possible, by combining like terms.

Front

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

Back

Isolating the 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 a contradiction in the context of equations?

Back

A contradiction occurs when the simplification of an equation leads to a false statement, indicating no solutions.