Justifying Equation Solving

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 for an equation to have 'no solution'?

Back

An equation has 'no solution' when there are no values for the variables that can satisfy the equation.

Front

What is an example of an equation with no solution?

Back

An example is 2x + 3 = 2x - 5, which simplifies to 3 = -5.

Front

What does it mean for an equation to have 'one solution'?

Back

An equation has 'one solution' when there is exactly one value for the variable that satisfies the equation.

Front

What is an example of an equation with one solution?

Back

An example is 2x + 3 = 7, which simplifies to x = 2.

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.

Front

What is an example of an equation with infinite solutions?

Back

An example is 3x + 6 = 3(x + 2), which simplifies to 0 = 0.

Front

What is the importance of checking solutions in equations?

Back

Checking solutions ensures that the values found satisfy the original equation, confirming their validity.

Front

What is a contradiction in the context of equations?

Back

A contradiction occurs when an equation simplifies to a false statement, indicating no solutions exist.

Front

What is the process of solving an equation?

Back

The process involves isolating the variable on one side of the equation to find its value.