Question

Select the correct answer. If x + 12 ≤ 5-y and 5-y≤ 2(x-3), then which statement is true? O A. x+12 ≤2(5-y) x+12 ≤ 2x-3 B. O c. O D. x+12 ≤y-5 x+12 ≤ 2(x − 3) mentum All rights reserved.​

Answer 1

the correct option would be,

x + 12 ≤ 2(x - 3)

Explanation:

x + 12 ≤ 5 - y and

5 - y ≤ 2(x - 3)

according to transitive property of inequality:

if x < y and

y < z

then x < z

thus, the correct option would be,

x + 12 ≤ 2(x - 3)

Answer 2

D. x+12 ≤ 2(x − 3)

Explanation:

The correct answer is: D. x+12 ≤ 2(x − 3)

We can solve this problem by graphing the inequalities. First, we rewrite the inequalities in terms of y:

x + 12 ≤ 5 - y

y ≤ -x + 17

5 - y ≤ 2(x - 3)

y ≥ 2x - 11

Now, we can graph the inequalities:

[asy]

unitsize(0.5 cm);

draw((-10,0)--(10,0));

draw((0,-10)--(0,10));

draw((-10,-17)--(10,17),Arrow(6));

draw((10,17)--(-10,17),Arrow(6));

draw((10,-11)--(-10,11),Arrow(6));

draw((-10,-11)--(10,-11),Arrow(6));

label("y=−x+17", (10,17), E);

label("y=2x−11", (-10,-11), W);

dot("(−3,5)", (-3,5), NW);

[/asy]

The shaded region represents the solutions to both inequalities. We can see that the only statement that is always true for the solutions in the shaded region is:

x + 12 ≤ 2(x - 3)

Therefore, the correct answer is D.