Question

10

Gary, Nancy, and Jamal are trying to write an inequality where all values in the set of numbers below make the inequality true.

{0, 1, 3, 4, 6, 12}

Consider their inequalities.

Gary: 6 > 0.50

Nancy: 30 -t < 18

Jamal: 12
Which student(s) wrote an inequality that is true for all values in the set of numbers? Select your answer from the drop-down list

Only Gary as the

Only Gary

Only Nancy

Only Jamal

Only Gary and

Nancy

Only Gary and

Jamal

Only Nancy and

Jamal

Answer 1

Jamal's inequality is correct

Explanation:

Given

`Sets:\{0,1,3,4,6,12\}`

Gary:
`6>0.5t`

Nancy:
`30 -t \le 18`

Jamal:
`12 \le t+12`

Required

Which of the inequalities is/are true

Gary:
`6>0.5t`

`6>0.5t`

Divide both sides by 0.5

`(6)/(0.5) > (0.5t)/(0.5)`

`12 > t`

Rewrite as:

`t < 12`

Gary's inequality is false because:
`12 = 12`

Nancy:
`30 -t \le 18`

`30 -t \le 18`

Collect like terms

`-t \le 18 - 30`

`-t \le -12`

Divide both sides by -1

`t \ge 12`

Nancy's inequality is incorrect because: 0,1,3,4 and 6 are less than 12

Jamal:
`12 \le t+12`

`12 \le t+12`

`12 - 12 \le t`

`0 \le t`

Rewrite as:

`t \ge 0`

Jamal's inequality is correct because: 0,1,3,4,6 and 12
`\ge 0`