Question

Which inequality is equivalent to this one?

y-8 <(with the line under it) -2

A. y-8+8 >(with the line under it) -2+8
B. y-8+8 < -2+8
C. y-8+2 <(with the line under it)-2+8
D. y-8+2 <(with the line under it)-2+2

Answer 1

The inequality which is equivalent to the given inequality is:

D.
`y-8+2\leq -2+2`

Explanation:

We are given a inequality as:

`y-8\leq -2`

which on simplifying gives.

i.e. on adding 8 on both side of the inequality we get:

`y\leq 6`

A)

`y-8+8\geq -2+8`

on simplifying we gets:

`y\geq 6`

which does not matches the actual inequality.

Hence, option: A is incorrect.

B)

`y-8+8<-2+8`

on solving we get:

`y<6`

which is not equivalent to the given inequality.

Hence, option: B is incorrect.

C)

`y-8+2\leq -2+8`

on simplifying we get:

`y-6\leq 6`

Now on adding both side of the inequality by 6 we get:

`y\leq 12`

which again does not matches.

Hence, option: C is incorrect.

D)

`y-8+2\leq -2+2`

on simplifying we get:

`y-6\leq 0\\\\i.e.\\\\\\y\leq 6`

It matches the actual expression.

Hence, option: D is correct.

Answer 2

D y-8 +2 ≤ -2+2

Explanation:

y-8 ≤ -2

Add 2 to each side

y-8 +2 ≤ -2+2