Question

Which compound equalities have x = 2 as a solution? Check all that apply

O 4 < 5x - 1 <10
O4 < 5x - 3 < 10
04 < 5x - 7 < 10
04 < 2x + 1 < 10
04 < 2x + 3 < 10
O 4 < 2x + 6 < 10

Answer 1

`(a)\ 4 < 5x - 1 < 10`

`(b)\ 4 < 5x - 3 < 10`

`(d)\ 4 < 2x + 1 < 10`

`(e)\ 4 < 2x + 3 < 10`

Explanation:

Required

Whose solution is
`x = 2`

`(a)\ 4 < 5x - 1 < 10`

Add 1 to both parts

`4 +1< 5x < 10+1`

`5< 5x < 11`

Divide through by 5

`1< x<2.2`

Substitute 2 for x

`1< 2<2.2` --- this is true

`(b)\ 4 < 5x - 3 < 10`

Add 3 to both parts

`4 +3< 5x < 10+3`

`7< 5x < 13`

Divide by 5

`1.4< x < 2.6`

Substitute 2 for x

`1.4 < 2 < 2.6` --- this is true

`(c)\ 4 < 5x - 7 < 10`

Add 7 to both parts

`4 +7< 5x < 10+7`

`12< 5x < 17`

Divide by 5

`2.4< x < 3.4`

Substitute 2 for x

`2.4< 2 < 3.4` --- this is false because 2.4 > 2

`(d)\ 4 < 2x + 1 < 10`

Subtract 1 from all parts

`4 - 1 <2x<10-1`

`3 <2x<9\\`

Divide by 2

`1.5 < x < 4.5`

Substitute 2 for x

`1.5 < 2 < 4.5` --- this is true

`(e)\ 4 < 2x + 3 < 10`

Subtract 3 from all parts

`4 -3< 2x < 10-3`

`1 < 2x < 7`

Divide by 2

`0.5 < x < 3.5`

Substitute 2 for x

`0.5 < 2 < 3.5` ----- this is true

`(f)\ 4 < 2x + 6 < 10`

Subtract 6 from all parts

`4 -6< 2x< 10-6`

`-2< 2x< 4`

Divide by 2

`-1< x< 2`

Substitute 2 for x

`-1< 2< 2` --- this is false because 2 = 2; not 2 < 2