Solving Equations with variables on both sides

In some equations we can see the variables on both sides. First get the variables to one side of the equation and a number on the other side of the equation.
*** Performing the same operation on both sides of an equation does not change the validity of the equation ***

Example : solve 6(b +5) = 48
Use distributive property: a ( b + c ) = a*b + a*c
6(b +5) = 48
6b + 30 = 48 (distributive property)
6b + 30 – 30 = 48 – 30 ( subtracting 30 from both sides)
6b = 18
6b / 6 = 18 / 6 (dividing both sides by 6)
b = 3

Practice:Solve
2( x + 2) = 10
3( x + 4) = 30
5(a – 2) = 0

Example : solve 4a + 3( a – 2) =1
4 a + 3 a – 6 = 1 (distributive property 3 (a – 2) = 3a – 6 )
7a – 6 = 1 ( combining like terms, 4a + 3a = 7a)
7a – 6 + 6 = 1 + 6 ( adding 6 to bothsides)
7a = 7
7a / 7 = 7 / 7 (dividing both sides by 7 )
a = 1

practice: solve
a + 2( a – 7) =1
3x + 4 ( x +2 ) = 22
7p – 3(p + 4 ) = 8


Example : solve 5x = 7 ( x -2)
5x = 7x – 14 (distributive property 7 (x – 2) = 7x – 14 )
5x – 7x = 7x - 7x - 14 (subtracting 7x from both sides to bring x terms one side)
-2x = -14
-2x / -2 = -14 /-2 ( dividing both sides by -2)
X = 7

Practice : solve
3x = 5 ( x -6)
8x = 6( x + 3)
9y = 5( y – 8)

Example: solve 2 ( x + 5 ) = 5 ( x-1)
2 x + 10 = 5x – 5 (distributive property )
2x + 10 – 10 = 5x – 5 – 10 ( subtracting 10 from both sides)
2x = 5x - 15
2x – 5x = 5x – 5x - 15 (subtracting 5x from both sides to bring x terms one side)
- 3 x = - 15
-3x / -3 = - 15 / - 3 ( dividing both sides by -3)
X = 5

Practice : solve
2 ( x - 5 ) = 6 (1- x )
5 ( y + 8 ) = 3 ( y + 20)
6 ( p – 8) = 2 ( 4- p )