Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

How do you isolate a variable in a linear equation?

Back

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side.

Front

What does it mean to solve a linear equation?

Back

Solving a linear equation means finding the value of the variable that makes the equation true.

Front

What is the first step in solving the equation 5 + 3x = 8x - 15?

Back

The first step is to get all terms involving x on one side and constant terms on the other side.

Front

What is the solution to the equation 5 + 3x = 8x - 15?

Back

The solution is x = 4.

Front

How do you check if your solution to a linear equation is correct?

Back

You substitute the solution back into the original equation to see if both sides are equal.

Front

What is the solution to the equation 12 = 20x - 18?

Back

The solution is x = 2.

Front

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

Back

The slope indicates the steepness of the line and the direction it goes. A positive slope means the line rises, while a negative slope means it falls.

Front

What is the solution to the equation 8x + 2 + 3x + 5 = x + 12?

Back

The solution is x = 1/2.

Front

What does it mean if a linear equation has no solution?

Back

It means that the lines represented by the equations are parallel and will never intersect.