Question

Choose the solution to this inequality. < 3 34 O A. y. -12 B. ys o o c. y< 1 / 3 O D. y> 4​

Answer 1

`\boxed{\boxed{\bf y < - \cfrac{1}{2}}}`

Option A

Explanation:

`\bf \: Given \: inequality :`

`\sf \implies \: \cfrac{4}{3 } \: y < \cfrac{ - 8}{3} \: y`

We need to find the solution to the inequality.

`\bf \: Solution:`

`\sf \implies \: \cfrac{4}{3 } \: y < \cfrac{ - 8}{3} \: y`

`\rm \: Firstly,Flip \: the \: inequality :`

`\sf \implies \cfrac{ - 8}{3} y > \cfrac{4}{3}`

`\rm \: Then,\; multiply\; each\: side \: \: by \: \cfrac{ - 3}{8} \: :`

`\sf \implies \: \cfrac{ - 8}{3}y * \cfrac{ 3}{ - 8} > \cfrac{4}{3} * \cfrac{ 3}{ - 8}`

`\rm \: Use \: cancellation \: method \: to \: cancel \: LHS:-`

Steps of cancelling :-

• Cancel -8( which is on the numerator) and -8 (on the denominator) :

`\sf \implies \cfrac{ \cancel{- 8}}{3}y * \cfrac{ 3}{ \cancel{- 8} } > \cfrac{4}{3} * \cfrac{ 3}{ - 8}`

• Cancel 3(which is on the numerator) and 3( which is on the denominator) :

`\sf \implies\cfrac{ \cancel{- 8}}{ \cancel3}y * \cfrac{ \cancel 3}{ \cancel{- 8} } > \cfrac{4}{3} * \cfrac{ 3}{ - 8}`

• Results to,

`\sf \implies \: 1y < \cfrac{4}{3} * \cfrac{3}{ - 8}`

As we know 1y equals to y. So,

`\sf \implies \: y < \cfrac{4}{3} * \cfrac{3}{ - 8}`

`\rm \: Now, Cancel \: the \: RHS :`

Steps of cancelling:-

• Cancel 3 (which is on the numerator) and cancel 3 (which is on the denominator):

`\sf \implies \: y < \cfrac{4}{ \cancel3} * \cfrac{ \cancel3}{ - 8}`

`\sf \implies{y} < 4 * \cfrac{1}{ - 8}`

• Cancel 4 and -8 :

`\sf \implies \: y < \cancel{4} * \cfrac{1}{ \cancel{ - 8}}`

• Results to,

`\sf \implies \: y < 1 × \cfrac{ - 1}{2}`

`\sf \implies \: y < \cfrac{ - 1}{2}`

`\rm \: Which \: can \: be \: rewritten \: as,`

`\sf \implies \: y < - \cfrac{1}{2}`

This matches with option A.

Hence, Option A is correct!

`\rule{225pt}{2pt}`

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