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 an 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 for x?

Back

Solving for x means finding the value of x that makes the equation true.

Front

What is the first step in solving the equation 2x + 5 = 12?

Back

The first step is to subtract 5 from both sides of the equation.

Front

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

Back

x = 3.5

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac. It allows you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you apply the distributive property to the equation 3(5x + 10)?

Back

You multiply 3 by both 5x and 10, resulting in 15x + 30.

Front

What is the solution to the equation 3(5x + 10) + 10 = 6x - (x + 10)?

Back

x = -5.

Front

What does it mean when an equation has no solution?

Back

An equation has no solution when the variable cancels out and results in a false statement, such as 0 = 5.

Front

What is the solution to the equation 7 - 5x = 12?

Back

x = -1.