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 (usually x) that makes the equation true.

Front

What is the first step in solving the equation 12 = 20x - 18?

Back

The first step is to isolate the term with the variable by adding 18 to both sides, resulting in 30 = 20x.

Front

How do you isolate x in the equation 30 = 20x?

Back

Divide both sides by 20 to get x = 30/20, which simplifies to x = 1.5 or x = 2.

Front

What is the solution to the equation 2(3x + 4) + 2 = 4 + 3x?

Back

The solution is x = -2.

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 simplify the equation 4x + 1 = 7x - 5?

Back

Subtract 4x from both sides to get 1 = 3x - 5, then add 5 to both sides to find x.

Front

What is the solution to the equation 7x + 5 + x - 3 + x = 5?

Back

The solution is x = 1/3.

Front

What is the process of combining like terms?

Back

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power.

Front

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

Back

The solution is x = 1/2.