Solving Equations with Special Solutions

Front

What is a solution set in an equation?

Back

The solution set is the set of all values that satisfy the equation.

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 infinitely many solutions?

Back

It means there are countless values that can satisfy the equation, often due to the equation being an identity.

Front

What is the first step in solving the equation 5 - 2(x - 7) = x + 1 + 3x?

Back

The first step is to distribute -2 to (x - 7).

Front

What is the solution to the equation 2(x + 5) = 2x + 5?

Back

no solution

Front

What is the solution to the equation 4x + 5 = 2(2x + 3)?

Back

no solution

Front

What is the solution to the equation 5 - 2(x - 7) = x + 1 + 3x?

Back

no solution

Front

What is the solution to the equation 2x + 3 = 2x + 3?

Back

infinitely many solutions

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 purpose 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.