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

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 2 − 4x = 3x − 12?

Back

The first step is to isolate the variable x by moving all terms involving x to one side of the equation and constant terms to the other side.

Front

Solve for x: 2 − 4x = 3x − 12

Back

x = 2

Front

What is the solution to the equation 10 = 3x − 12?

Back

x = 22/3

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

Solve for x: 4(x + 8) − 4 = 34 − 2x

Back

x = 1

Front

What is the purpose of combining like terms in an equation?

Back

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

Front

Solve for x: 2x + 5 = 12

Back

x = 7/2

Front

What does it mean to isolate the variable in an equation?

Back

Isolating the variable means to manipulate the equation so that the variable is on one side by itself, making it easier to find its value.