Front

What is an equation with one solution?

Back

An equation with one solution is a linear equation that can be solved to yield a single unique value for the variable. For example, the equation 2x + 3 = 7 has one solution: x = 2.

Front

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

Back

An equation has no solutions when there is no value for the variable that can satisfy the equation. This often occurs when the equation simplifies to a false statement, such as 0 = 5.

Front

What is an equation with infinitely many solutions?

Back

An equation with infinitely many solutions is one where any value of the variable satisfies the equation. This typically happens when the equation simplifies to a true statement, such as 0 = 0.

Front

How do you determine if an equation has no solutions?

Back

To determine if an equation has no solutions, simplify the equation and check if it leads to a contradiction, such as a false statement (e.g., 5 = 0).

Front

What is the first step in solving a linear equation?

Back

The first step in solving a linear equation is to isolate the variable on one side of the equation, often by using inverse operations.

Front

What is the significance of coefficients in linear equations?

Back

Coefficients are the numerical factors that multiply the variables in an equation. They affect the slope and position of the line represented by the equation.

Front

What is the process of combining like terms in an equation?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power to simplify the equation.

Front

What does it mean to isolate a variable?

Back

Isolating a variable means rearranging the equation so that the variable is alone on one side, making it easier to solve for its value.

Front

What is the role of the distributive property in solving equations?

Back

The distributive property allows you to multiply a single term by each term inside a set of parentheses, which helps simplify equations.

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.