Which of the following points is a solution to the linear inequality y≤2x−445?

Question

a. (−17,−3812)
b. (1/2,−3)
c. (−3,−10)
d. (1/2,−5)

Answer 1

To determine which of the given points is a solution to the linear inequality $y\le 2x-445$, we will substitute each point into the inequality and check whether it holds true.

1. For point (−17,−3812): $$y=-3812\text{and}x=-17$$ Substitute into the inequality: $$-3812\le 2(-17)-445$$ Calculate the right side: $$2(-17)=-34\text{so, }-34-445=-479$$ Now compare: $$-3812\le -479\text{(false)}$$

2. For point (1/2,−3): $$y=-3\text{and}x=1/2$$ Substitute into the inequality: $$-3\le 2(1/2)-445$$ Calculate the right side: $$2(1/2)=1\text{so, }1-445=-444$$ Now compare: $$-3\le -444\text{(false)}$$

3. For point (−3,−10): $$y=-10\text{and}x=-3$$ Substitute into the inequality: $$-10\le 2(-3)-445$$ Calculate the right side: $$2(-3)=-6\text{so, }-6-445=-451$$ Now compare: $$-10\le -451\text{(false)}$$

4. For point (1/2,−5): $$y=-5\text{and}x=1/2$$ Substitute into the inequality: $$-5\le 2(1/2)-445$$ Calculate the right side: $$2(1/2)=1\text{so, }1-445=-444$$ Now compare: $$-5\le -444\text{(true)}$$

Thus, the only point that satisfies the inequality $y\le 2x-445$ is (1/2,−5).

Therefore, the solution is: d. (1/2,−5).