Question

Amy thinks the answer to the inequality negative 5X -12 is less than or equal to 18 is X less than or equal to -6. Bryan thinks the answer is X greater than or equal to -6. Decide who is correct. Explain your thinking.

Answer 1

Amy is correct in her answer.

Explanation:

Here, the given expression is:

5X - 2 ≤ 18

The answer quoted by Amy = X ≤ -6

⇒ Possible values of X = -6, -7, -8, -9, -10,...

The answer quoted by Bryan = X ≥ -6

⇒ Possible values of X = -6, -5, -4, -3, -2, ...., 4, 5, 6, 7..

Now, simplifying the given inequality,

5X - 2 ≤ 18 ⇒ 5X - 2 + 2 ≤ 18 + 2

or, 5X ≤ 20

or, X ≤ 20/5 = 4

⇒ X ≤ 4

Hence, the possible values of X = 4, 3, 2, 1, 0, -1, -2, .....

So, from above answers, X ≤ -6 is the most appropriate answer

as here,all possible values of x are less than 4.

Hence, Amy is correct in her answer.