Linear Equations                                                 -- Section 1.1 --

  Solve for x:   x + 12 = 18

Solve

Step

Check 

 
Subtract 12 from
both sides

If x = 6, then
6 + 12  = 18
     18 = 18 

Solve for x:   x + 5 = 20

[Solution]

    Solve for x:   3x – 9 = 7

Solve

Step

Check 


Add 9 to both sides

Divide by 3 

  Solve for x:   2x – 8 = 19  

[Solution]

Solve for x:  5(x – 2) + 3 = 2(3x – 1)

Solve

Step

Check 

5(x – 2) + 3 = 2(3x – 1) Original equation

If x = -5, then
 5x – 10 + 3 = 6x – 2 Distributive Property
     a(b – c) = ab – ac

5(-5 – 2) + 3 = 2(3(-5) – 1)

         5x – 7 = 6x – 2
       -6x + 7   -6x + 7 
        -x + 0  =   0  + 5 		Combine Like Terms
Subtract 6x , Add 7 
      to both sides

            5(-7) + 3 = 2(-15 – 1)
               -35 + 3 = 2(-16)
                     -32 = -32

-x = 5   
  x = -5

 Multiply both sides by -1
      -x = -1 × x

Solve for x:   6(x – 1) + 4 = 2(4x + 1) 

[Solution]

  Solve for x:  x + 4 = x + 8

Solve

Step

Check 

              x + 4 = x + 8

 Original equation

No solution

              x + 4 = x + 8
            -x         -x       
                    4 ¹ 8

 Subtract x from both sides
But 4 ¹ 8		 There is no number plus 4 can equal the same number plus 8

Solve for x:   2x + 3 = 2x – 4

[Solution]
Not all linear equations have solutions.  Can you think of an linear equation that would have more than one solutions?

Solve for x: 

Solve

Step

Check 

Original equation

  

Multiply both sides by the LCD, 15, to clear fractions.

Divide by 11

LCD = 3 × 5 × 1 = 15
4 can be written as 4/1

Rewrite as

 

[Solution]

  Solve for x: 

Solve

Step

Factor denominator. Note: x can not be 5 or -5.  You can't have zero in the denominator.
Multiply both sides by the LCD to clear fractions.
LCD = (x + 5)(x – 5)

4(x – 5) + 2(x + 5) = 32

Check 

4x – 20 + 2x + 10 = 32
6x – 10 = 32

6x = 42
x = 7

  Solve for x: 

[Solution]

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada