Question

Which ordered pair is a solution to the linear inequality?
y - 4 x < -6

(-2,4)
(1, -2)
(1, 3)
(2, 3)

Answer 1

Answer: Choice B (1,-2)

note: I'm assuming there is a "less than or equal to" sign as part of the given inequality, rather than a simple "less than" sign (without the "or equal to" part)

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Work Shown:

Plug in x = -2 and y = 4 from the point (x,y) = (-2, 4). Then simplify. If you get a true statement, then this is a solution point

$y - 4x \le -6$

$4 - 4*(-2) \le -6$

$4 + 8 \le -6$

$12 \le -6$

This statement is false. The value 12 is not to the left of -6 on the number line, nor is 12 equal to -6. So (x,y) = (-2,4) is not a solution

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Plug in x = 1 and y = -2

$y - 4x \le -6$

$-2 - 4*(1) \le -6$

$-2 - 4 \le -6$

$-6 \le -6$

This statement is true, but only if the inequality sign is a "less than or equal to" sign. Otherwise, the statement is false because -6 cannot be smaller than itself.

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Plug in x = 1 and y = 3

$y - 4x \le -6$

$3 - 4*(1) \le -6$

$3 - 4 \le -6$

$-1 \le -6$

Like choice A, this is false. So (x,y) = (1,3) is not a solution

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Plug in x = 2 and y = 3

$y - 4x \le -6$

$3 - 4*(2) \le -6$

$3 - 8 \le -6$

$-5 \le -6$

We end up with another false statement. So (x,y) = (2,3) isn't a solution either.