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 7 − 5x = 12?

Back

The first step is to isolate the term with the variable by moving the constant to the other side: -5x = 12 - 7.

Front

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

Back

The solution is x = -1.

Front

How do you solve the equation 5x = -35?

Back

Divide both sides by 5 to isolate x: x = -35 / 5.

Front

What is the solution to the equation 5x = -35?

Back

The solution is x = -7.

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 6(2x + 1) = 18?

Back

Multiply 6 by both 2x and 1: 12x + 6 = 18.

Front

What is the solution to the equation 6(2x + 1) = 18?

Back

The solution is x = 1.

Front

What is the process to solve the equation 15x + 40 = 5x − 10?

Back

First, move all terms involving x to one side and constant terms to the other side: 15x - 5x = -10 - 40.