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, and 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 for x in an equation?

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 7x + 5 + x - 3 + x = 5?

Back

Combine like terms on the left side of the equation.

Front

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

Back

x = 1/3.

Front

What is the significance of the distributive property in solving equations?

Back

The distributive property allows you to multiply a single term by each term inside a set of parentheses, which is essential for simplifying equations.

Front

How do you solve the equation -12(x - 1) = -3(x - 1)?

Back

Factor out (x - 1) and then solve for x.

Front

What is the solution to the equation -12(x - 1) = -3(x - 1)?

Back

x = 1.

Front

How can you express y in terms of x in the equation 2x + 2y = 18?

Back

Rearranging gives y = -x + 9.

Front

What is the purpose of multiplying both sides of an equation by the same number?

Back

It maintains the equality of the equation while simplifying it.