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Order of Operations

In the expres...

Question

In the expression $2.5 + 0.05 - [1.6 - {3.2 - (3.2 + 2.1 \div x)}] = 0.65$ , find the value of $x$ .

A

8

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B

9

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C

6

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D

7

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Solution

The correct option is D 7
Given $2.5 + 0.05 - [1.6 - {3.2 - (3.2 + \frac{2.1}{x})}] = 0.65$
$\Rightarrow 2.5 + 0.05 - [1.6 - {3.2 - 3.2 - \frac{2.1}{x}}] = 0.65$
$\Rightarrow 2.55 - [1.6 + \frac{2.1}{x}] = 0.65$
$\Rightarrow 2.55 - 1.6 - \frac{2.1}{x} = 0.65$
$\Rightarrow 0.95 - \frac{2.1}{x} = 0.65 \Rightarrow \frac{2.1}{x} = 0.95 - 0.65 = 0.30 \Rightarrow x = \frac{2.10}{0.30} = \frac{210}{30} = 7$

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Similar questions

Q. Find the value of

x

in the following expression

6.4 \times 2.5 + 2.1 \div x = 26.

	A	A	B	B	C	C	D	D	E	E
	M	S	M	S	M	S	M	S	M	S
$2006$	$2.8$	$1.3$	$3.3$	$2.2$	$2.6$	$1.7$	$3.0$	$2.2$	$1.9$	$1.4$
$2007$	$3.2$	$2.0$	$2.4$	$1.6$	$2.2$	$1.5$	$2.5$	$1.9$	$2.0$	$1.7$
$2008$	$1.9$	$0.9$	$2.9$	$1.6$	$2.1$	$1.0$	$2.3$	$1.5$	$1.6$	$1.1$
$2009$	$1.0$	$0.4$	$2.4$	$1.3$	$2.8$	$1.4$	$2.1$	$1.2$	$3.2$	$2.5$
$2010$	$2.5$	$1.5$	$2.3$	$1.2$	$2.6$	$2.1$	$1.8$	$1.1$	$3.1$	$2.6$

What is the total number of units manufactured by company C over all the years together?

\frac{2.5 \times 1.5}{3.2 \times 0.2}

Q. Evaluate (3.2x⁶y³) × (2.1x²y²) when x = 1 and y = 0.5

Ans

First multiply the expressions and then substitute the values for the variables.

To multiply algebric experssions use the commutative and the associative laws along with the law of indices,

a^{m} \times a^{n} = a^{m + n}

(3.2 x^{6} y^{3}) \times (2.1 x^{2} y^{2}) = (3.2 \times 2.1) \times (x^{6} \times x^{2}) \times (y^{3} \times y^{2}) = 6.72 x^{8} y^{5}

(3.2 x^{6} y^{3}) \times (2.1 x^{2} y^{2}) = 6.72 x^{8} y^{5}

Now, substitute 1 for x and 0.5 for y in the result.

6.72 x^{8} y^{5} = 6.72 {(1)}^{8} {(0.5)}^{5} = 6.72 \times 1 \times 0.03125 = 0.21

Hence, the answer is

0.21

Q. Answer the question based on the information given in the following table A,B, C, D, E denote companies and 2006, 2007, 2008, 2009 and 2010 denote years.
Number of units manufactured(M) and Number of units sold (s)(in hundred) by five different companies over the years.

	A	A	B	B	C	C	D	D	E	E
	M	S	M	S	M	S	M	S	M	S
$2006$	$2.8$	$1.3$	$3.3$	$2.2$	$2.6$	$1.7$	$3.0$	$2.2$	$1.9$	$1.4$
$2007$	$3.2$	$2.0$	$2.4$	$1.6$	$2.2$	$1.5$	$2.5$	$1.9$	$2.0$	$1.7$
$2008$	$1.9$	$0.9$	$2.9$	$1.6$	$2.1$	$1.0$	$2.3$	$1.5$	$1.6$	$1.1$
$2009$	$1.0$	$0.4$	$2.4$	$1.3$	$2.8$	$1.4$	$2.1$	$1.2$	$3.2$	$2.5$
$2010$	$2.5$	$1.5$	$2.3$	$1.2$	$2.6$	$2.1$	$1.8$	$1.1$	$3.1$	$2.6$

What is the average number of units sold by company D over all the years together?

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