Question

4 Which of the following expressions has asolution of -2?1. (-23 . 3) = 3 3 3II. 28 + (-2.40.08)III. 24[3+(-19)]F.ll onlyG I and II onlyH II and III onlyJ I, II, and III

Answer 1

In order to solve this question, let's develop each of the given expressions to find their solutions:

I. Notice that the numbers are presented in the form of an integer and a fraction part. We can rewrite them as:

`(-2(2)/(5)\cdot3)\colon3(3)/(5)=\lbrack-(2+(2)/(5))\cdot3\rbrack\colon(3+(3)/(5))`

Now, to solve the sums, we need to write both numbers in the sum with the same denominator, that is, 5:

`\begin{gathered} \lbrack-(2+(2)/(5))\cdot3\rbrack\colon(3+(3)/(5))=\lbrack-((10)/(5)+(2)/(5))\cdot3\rbrack\colon((15)/(5)+(3)/(5)) \\ =(-(12)/(5)\cdot3)\colon((18)/(5)) \end{gathered}`

Then, we need to use the property:

(a/b) : (c/d) = (a/b) . (d/c)

And we obtain:

`(-(12)/(5)\cdot3)\colon((18)/(5))=(-(12\cdot3)/(5))\cdot((5)/(18))=(-36)/(18)=-2`

II. 28 + (-2.4 : 0.08) = 28 - 240/8 = 28 - 30 = -2

III. We solve this in the same way we did for the first one:

`\begin{gathered} 2(1)/(4)\lbrack(7)/(3)+(-1(4)/(9))\rbrack=(2+(1)/(4))\cdot\lbrack(7)/(3)-(1+(4)/(9))\rbrack=((8)/(4)+(1)/(4))\cdot\lbrack(7)/(3)-((9)/(9)+(4)/(9))\rbrack \\ \\ =(9)/(4)\cdot((7)/(3)-(13)/(9))=(9)/(4)\cdot((21)/(9)-(13)/(9))=(9)/(4)\cdot(8)/(9)=(8)/(4)=2 \end{gathered}`

Therefore, I and II only have a solution of -2.

Answer: option G