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. For example, in the equation 2x + 3 = 7, subtract 3 from both sides and then divide by 2.

Front

What does it mean if a linear equation has infinite solutions?

Back

A linear equation has infinite solutions if it simplifies to a true statement for all values of the variable, such as 4x + 10 = 4x + 10.

Front

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

Back

A linear equation has no solution if it simplifies to a false statement, such as 3x + 3 = 3x + 2, where the variable cancels out and leaves a contradiction.

Front

Solve for x: 7x + 19 = -2x + 55

Back

x = 4

Front

Solve for x: 8x + 2 + 3x + 5 = x + 12

Back

x = 1/2

Front

What is the first step in solving the equation 3x + 3 = 6x + 6?

Back

The first step is to move all terms involving x to one side and constant terms to the other side, typically by subtracting 3x from both sides.

Front

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

Back

The equation has infinite solutions because it is true for all values of x.

Front

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

Back

The equation has no solution because it simplifies to 3 = 2, which is a contradiction.

Front

What is the purpose of combining like terms in a linear equation?

Back

Combining like terms simplifies the equation, making it easier to isolate the variable and solve.