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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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