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:

Jamal's inequality is correct

Step-by-step explanation:

Given

[tex]Sets:\{0,1,3,4,6,12\}[/tex]

Gary: [tex]6>0.5t[/tex]

Nancy: [tex]30 -t \le 18[/tex]

Jamal: [tex]12 \le t+12[/tex]

Required

Which of the inequalities is/are true

Gary: [tex]6>0.5t[/tex]

[tex]6>0.5t[/tex]

Divide both sides by 0.5

[tex]\frac{6}{0.5} > \frac{0.5t}{0.5}[/tex]

[tex]12 > t[/tex]

Rewrite as:

[tex]t < 12[/tex]

Gary's inequality is false because: [tex]12 = 12[/tex]

Nancy: [tex]30 -t \le 18[/tex]

[tex]30 -t \le 18[/tex]

Collect like terms

[tex]-t \le 18 - 30[/tex]

[tex]-t \le -12[/tex]

Divide both sides by -1

[tex]t \ge 12[/tex]

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

Jamal: [tex]12 \le t+12[/tex]

[tex]12 \le t+12[/tex]

[tex]12 - 12 \le t[/tex]

[tex]0 \le t[/tex]

Rewrite as:

[tex]t \ge 0[/tex]

Jamal's inequality is correct because: 0,1,3,4,6 and 12 [tex]\ge 0[/tex]

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