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

Answer:

Jamal's inequality is correct

Step-by-step 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

$\frac{6}{0.5} > \frac{0.5t}{0.5}$

$12 > t$

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 $\ge 0$