Solving Linear Equations Part 1 A Linear Equation

Solving Linear Equations – Part 1 • A Linear Equation in One Variable is any equation that can be written in the form • To solve such a linear equation means to find the value of the variable (x in this case) that makes the equation true.

• Example 1 Solve The goal is to isolate the variable x on a side by itself. There are two numbers that prevent the x from being on a side by itself: The 3 is called the coefficient of the variable … … and the -4 is called the constant term. We will always eliminate the coefficient last.

Since the 3 (coefficient) is last, we want to work with the -4 first. Since the -4 is added to the variable term, we will add the opposite, or +4, to both sides of the equation.

Now, the coefficient of 3 is eliminated to isolate the x. Since the 3 is multiplied times the variable x, to eliminate it we must do the opposite, or divide both sides of the equation by 3.

Let’s check our solution: Substitute 4 for x …

• Example 2 Solve The goal is to isolate the variable x on a side by itself. There are two numbers that prevent the x from being on a side by itself: The -4 is the coefficient, which is eliminated last … … and the 7, or constant term will be eliminated first.

Since the 7 is added to the variable term, we will add the opposite, or -7, to both sides of the equation.

Since the -4 is multiplied times the variable x, to eliminate it we must do the opposite, or divide both sides of the equation by -4.

Let’s check our solution: Substitute -3/2 for x …