Linear Equations by Example  Part 1.1 
Solve for x: x + 12 = 18  
Solve 
Step 
Check 


If x = 6, then 

Solve for x: x + 5 = 20  
[Solution] 

Solve for x: 3x – 9 = 7  
Solve 
Step 
Check 

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) 

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 
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 
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 = 42 





Solve for x:  
[Solution] 

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joe mcdonald
Last Update 09.23.2010