Solving Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form ax + b = c, where a, b, and c are constants.

Front

What does it mean to solve a linear equation?

Back

To solve a linear equation means to find the value of the variable that makes the equation true.

Front

What is the first step in solving the equation 3x - x + 4 = 4(2x + 1)?

Back

Combine like terms on the left side and distribute on the right side.

Front

What is the solution to the equation 3(3x - 6) = 18?

Back

x = 4.

Front

What does it mean if an equation has no solution?

Back

It means that there is no value for the variable that can satisfy the equation.

Front

What does it mean if an equation has all real numbers as a solution?

Back

It means that any value for the variable will satisfy the equation.

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 isolate a variable in an equation?

Back

You isolate a variable by performing inverse operations to get the variable alone on one side of the equation.

Front

What is the next step to solve the equation 3x + 6 = 10 + 7x?

Back

Subtract 7x from both sides of the equation.

Front

What is the solution to the equation 2x + 3(5x - 7) = 47?

Back

x = 4.