Question

Which of the following pairs of inequalities are equivalent

x-5> 4 and 2x-10 >8

x- 5 >4 and 2x +10 >8

x+5 >4 and 2x+10 <8

ALL​

Answer 1

(a):
`x-5> 4` and
`2x-10 >8`

Explanation:

Given

Pairs of inequalities

Required

Select which is equivalent

(a):
`x-5> 4` and
`2x-10 >8`

Multiply both sides of
`x-5> 4` by 2

`2 * (x - 5) > 4 *2`

`2 * x - 2*5 > 4 *2`

`2x - 10 > 8`

Hence:
`x-5> 4` is equivalent to
`2x - 10 > 8`

(b):
`x-5> 4` and
`2x+10 >8`

Multiply both sides of
`x-5> 4` by 2

`2 * (x - 5) > 4 *2`

`2 * x - 2*5 > 4 *2`

`2x - 10 > 8`

Hence:
`x-5> 4` is not equivalent to
`2x+10 <8`

(c):
`x+5> 4` and
`2x+10 <8`

Multiply both sides of
`x+5> 4` by 2

`2 * (x + 5) > 4 *2`

`2 * x + 2*5 > 4 *2`

`2x + 10 > 8`

Hence:
`x+5> 4` is not equivalent to
`2x+10 <8`