Solving Equations with No and Infinite Solutions

Front

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

Back

An example is 2(n + 2) = 4n + 1 - 2n, which simplifies to a contradiction.

Front

What does it mean for an equation to have infinite solutions?

Back

An equation has infinite solutions when any value for the variable satisfies the equation, often resulting in an identity.

Front

What is an example of an equation with infinite solutions?

Back

An example is 3x + 6 = 3(x + 2), which simplifies to a true statement for all x.

Front

How can you determine if an equation has no solution?

Back

You can determine if an equation has no solution by simplifying it to a contradiction, such as 0 = 5.

Front

What is the first step in solving a linear equation?

Back

The first step is to simplify both sides of the equation, combining like terms and eliminating parentheses.

Front

What is the significance of isolating the variable in an equation?

Back

Isolating the variable helps to find its value by getting it alone on one side of the equation.

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 solution to the equation 4y = 38 - (1/2)(4y + 16)?

Back

The solution is y = 5.

Front

What is the solution to the equation 4(2r - 1) = -2(3r + 16)?

Back

The solution is r = -2.