Math 7 (Period 4)

Solving Equations Involving Negative Coefficients 4.3

The following show two different methods for solving an equation involving a negative coefficient. You can use whichever method you prefer.

Solve 8 – x = 3

First please note--> that the 8 is positive. Many students attach the negative sign to the 8.
That is NOT CORRECT! The subtraction sign (or negative sign) is attached to the x.
It is really -1 times x but we simply write –x. The -1 is understood to be part of the coefficient.

You can rewrite it so that you read...

Method 1

8 + (-1)x = 3

Now you need to isolate the variable—first step would be to subtract 8 for both sides

Usually we stack these but here I am showing you a horizontal approach

8 + (-1)x -8  = 3- 8

(-1)x = -5

Divide each side by -1

(-1)x/-1 = -5/-1

x = 5

Method 2

Move the variable term to the right side FIRST!

8 = 3 + x

Now we need to subtract 3 from both sides

8 -3 = 3 + x – 3

5 = x

or x = 5

Solving a Two- Step Equation

Solve 3 -2x = 11

Again you can use either of the two different methods above.  With the second method, you move the variable over first to obtain a positive variable.

Method 1

3-2x = 11

You would subtract 3 from both sides

3 -2x -3 = 11-3

-2x = 8

Method 2

3-2x =11

3= 11+ 2x

-8 = 2x

 

-4 = x