Answer

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**Hint:**We are going to use the BODMAS rule in solving this question. The BODMAS rule says that whenever we have to simplify a mathematical expression, then we will solve that expression according to the order of the bracket, after that order or power, after that division, after that division, after that multiplication, then addition and then subtraction. After using this rule, we will get the answer.

**Complete step by step solution:**

The question has asked us to evaluate the term \[\left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2\] or we can say that we have to simplify the term \[\left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2\].

We will use the BODMAS rule.

The mathematical expression we are going to solve is \[\left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2\].

We can see that, in the above expression there are brackets, division, multiplication, subtraction and addition.

We will solve them according to the order of BODMAS.

We will first solve which is inside the big bracket (that is this ‘[]’ bracket) bracket. The term which is inside the big bracket is \[\left( 30+6 \right)-32\]. So, we will first solve this.

Now, we can see that inside the big bracket, we have another bracket. Hence, we will solve which is inside of another bracket.

So, we can write

\[\left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2=\left[ 36-32 \right]\div 9\cdot 2\]

Now, we will solve which is inside the bracket.

\[\Rightarrow \left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2=4\div 9\cdot 2\]

Now, we have only left division and multiplication.

So, we will first use divide expression to solve according to the BODMAS rule.

Hence, the above equation can also be written as

\[\Rightarrow \left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2=\dfrac{4}{9}\cdot 2\]

The above equation can also be written as

\[\Rightarrow \left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2=\dfrac{4}{9}\times 2\]

Now, we will use multiply expression

\[\Rightarrow \left[ \left( 30+6 \right)-32 \right]\div 9\cdot 2=\dfrac{8}{9}\]

Hence, we have found the answer.

The answer is \[\dfrac{8}{9}\].

**Note:**

We should have a better knowledge in the topic of algebra to solve this type of question easily. We have used the BODMAS rule. Always remember that whenever there is a bracket in the mathematical expression, we will first solve the bracket or we will first solve the mathematical expression inside the bracket, after that we will solve the powers and then division, then multiplication, then addition and then subtraction. Remember that the term \[\dfrac{x}{y}\] can also be written as \[x\times \dfrac{1}{y}\].

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