Solving Linear Equations – Part 2

• A Linear Equation in One Variable is any equation that can be written in the form

ax b c

• It is assumed that you have already viewed Part 1 and know how to solve an equation of this form.

• Our goal with the more difficult linear equations is to write them in the above form and then complete the solution as in Part 1.

• Example 1

The first step is to combine the two variable terms on the left hand side. Let’s eliminate the variable x on the right side.

To do this, add the opposite, or –x, to both sides.

Solve 3 4 8x x

3 4 8xx x x

2 4 8x

Now solve as shown in Part 1.

2 4 8x

42 4 8 4x

2 4x

2 4

2 2

x

2x

Let’s check our solution:

2x

Substitute -2 for x …

3 4 8x x

2 823 4

6 4 10

10 10

• Example 2

Simplify each side.

Solve 3( 2) 8 5(2 1) 2x x

3 6 8 10 5 2x x

3 14 10 3x x

3( 2) 8 5(2 1) 2x x

Combine the variable terms.

3 14 10 3x x

3 14 10 10 0 31x x x x

7 14 3x

3 14 10 3x x

Isolate the x.

147 14 3 14x

7 11x

7 11

7 7

x

11

7x

7 14 3x

SUMMARY

• To solve a linear equation:

1) Simplify both sides of the equation.

2) Combine the variable terms.

3) The equation is now in the form ax b c

Isolate the x:a) Add the opposite of b to both sides.b) Divide both sides by a.