Parentheses Rules Definition

Parentheses are used in Algebraic / Mathematical expressions primarily to modify the normal order of operations. Therefore in an expression involving parentheses, the terms present inside the parentheses () are evaluated first.

There are some basic parentheses Rules presented below. You must learn them by heart.

 `a+(-b)=a-b`

 `a- (-b) = a+b `

 `a * (-b) =-ab`

 `(-a)(-b)=ab`


We present some examples involving Parentheses Rules that will help you understand their significance and the way they are used.


Parentheses Rules Examples


Example 1:
 2

Explanation:

The given expression involves two parentheses. We can solve them both separately, and then combine their results as indicated by the expression.

  • `(2+4*2)-(3+5)`

    = (2+8)-(3+5)
  • = 10-(3+5)
  • = 10-8
  • = 2

Example 2:
 8

Explanation:

In the given expression, we have two parentheses: one inside the other. In this case, we first solve the inner parentheses and then combine the result with other terms to evaluate the outer brackets.

  • (2+4*(5-2))+(2* (-3))

    = (2+4*3)+(2* (-3))
  • = (2+12)+(2*(-3))
  • = 14+(2*(-3))
  • = 14+(-( 2*3 )) since a . ( -b) =-ab
  • = 14+( -6)
  • 14-6 since a+( -b) = a-b
  • = 8

Example 3:
 4x-1

Explanation:

  • 3+4(x-1)

    = 3+4(x)+4(-1)
  • (We have used distributive property here)
  • = 3+4x-4
  • since `a*(-b) =-ab`
  • = 3+4(x-1) = 4x-1

Example 4:
 7

Explanation:

We are given that

6x+5-x = 7x+(-9)

In order to simplify the expression, we combine like terms using parentheses.

=> (6-1) x+5 = 7x-9

=> 5x+5 = 7x-9

=> 5x-5x+5 = 7x-5x-9

(Subtract 5x from both sides)

=> 5 = (7-5)x-9

=> 5 = 2x-9

=> 5+9 = 2x-9+9

(Add 9 to both sides)

=> 14 = 2x

=> 7 = x

(Divide on both sides by 2)


Example 5:
  5/2

Explanation:

We are given that

- (-2x)+6+(- x) = 3x-(-1)

In order to find the value of x, we will first simplify the given expression. It seems that simplifying the +ve and -ve signs can be really helpful

As we have learned that

`a-(-b) = a+b`

We use this simple formula in our expression to give

+ 2x+6+(- x) = 3x+1

Next we make use of a+( -b) = a-b

2x+6-x = 3x+1

Next we combine the like terms on both sides

(2-1)x+6 = 3x+1

x+6 = 3x+1

x-x+6 = 3x-x+1 (Subtracting*from both sides)

6 = (3-1)x+1

6 = 2x+1

6-1 = 2x+1-1 (Subtracting 1 from both sides)

=> 2x = 5

=>x= 5/2 (Dividing on both sides by 2)






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