Which of the following is a solution of y > |x| - 5?
(4, -1)
(-1, -4)
(-4, 1)

(-4, 1) is the solution to given inequality

Solution:

Given inequality is:

y > | x | - 5

The modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign

Let us check the options

Option A

Substitute (x, y) = (4, -1) in given inequality and check if it satisfies the inequality

-1 is equal to -1

Thus the inequality is not satisfied

Thus (4, -1) is not the solution

Option B

Substitute (x, y) = (-1, -4) in given inequality

But -4 is equal to -4

So the inequality is not satisfied. Thus (-1, -4) is not a solution

Option C

Substitute (x, y) = (-4, 1) in given inequality

1 is greater than -1

Thus the inequality is satisfied

Thus (-4, 1) is the solution

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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