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Linear Equations

The Addition Property of Equality

If a= b, then a+ c= b+ c

Solve the equation x–7 = 13

By adding 7 to both sides of the equation we can isolate the variable

x–7 + 7= 13 + 7
x= 20


Check the solution . Is 20 –7 = 13 ?

Solve the equation x+ 12 = 21

By adding –12 to both sides of the equation we can isolate the variable

x+ 12 + (–12) = 21 + (–12)
x= 9


Check the solution. Is 9 + 12 = 21 ?

The Multiplication Property of Equality

If a = b, then ac = bc

Solve the equation

By multiplying both sides of the equation by 7 we can isolate the variable.

Check the solution. Is

If a = b, then ac = bc

Solve the equation 3x = 21

By multiplying both sides of the equation by we can isolate the variable.

Check the solution. Is 3(7) = 21 ?

Solve the equation 5x – 7 = 68

Add 7 to both sides of the equation (do additions and subtractions first .)

Multiply both sides of the equation by

Check the solution. Is 5(15) – 7 = 68 ?

Solve the equation –3x + 8 = 47

Add –8 to both sides of the equation.

Multiply both sides of the equation by

Check the solution. Is –3(–13) + 8 = 47 ?

Solve the equation 2(x + 7) – 5x = –25

Distribute to remove the parentheses

2x + 14 – 5x = –25

Add like terms on the left side.

–3x + 14 = –25

Add –14 to both sides of the equation.

Multiply both sides of the equation by

Check the solution. Is 2(13 + 7) – 5(13) = –25 ?

Solve the equation –3(2x – 1) – 2x = 2(6x – 4) – 9

Distribute to remove the parentheses

–6x + 3 – 2x = 12x – 8 – 9  
   
Add like terms on the both sides
   
–8x + 3 = 12x – 17 Check the solution.
   
Add 8x to both sides of the equation Is –3(2(1) – 1) – 2(1) = 2(6(1) – 4) – 9 ?

3 = 20x – 17

Add 17 to both sides of the equation

20 = 20x

Multiply both sides of the equation by

Solve the equation

Find the common denominator and multiply both sides of the equation by it.

Another way
   
   
Add −14x to both sides of the equation. Find the common denominator
   
 
Add − 45 to both sides of the equation.
   
   
Multiply both sides of the equation by  
   
Multiply by the reciprocal
   
 

 

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