Solving multi-step problems using linear equations in one variable

Front

What is a linear equation in one variable?

Back

An equation that can be written in the form ax + b = 0, where a and b are constants and x is the variable.

Front

What does it mean if an equation has no solution?

Back

It means that there are no values for the variable that can satisfy the equation.

Front

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

Back

It means that any value for the variable will satisfy the equation, often resulting from an identity.

Front

What is an identity in mathematics?

Back

An equation that is true for all values of the variable, such as x + 2 = x + 2.

Front

How do you determine the number of solutions for the equation 2x + 1 = 2x - 1?

Back

By simplifying, you find that 1 = -1, which is a contradiction, indicating no solution.

Front

What is the solution to the equation 5n - 1 = 5n + 4?

Back

There is no solution, as simplifying leads to -1 = 4, which is false.

Front

What does it mean if two linear equations are parallel?

Back

They have the same slope but different y-intercepts, resulting in no points of intersection (no solution).

Front

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

Back

Combine like terms and simplify both sides of the equation.

Front

What is the solution to the equation x + 2 = x + 4?

Back

No solution, as simplifying leads to 2 = 4, which is false.

Front

What is the significance of the variable in a linear equation?

Back

The variable represents an unknown value that we are trying to solve for.