For nonzero integers, a, b, prove the following properties of divisibility and gcds. (you may use the fact that gcd(a, b) is an integer linear combination of a and b. you may not appeal to uniqueness of prime factorization because the properties below are needed to prove unique factorization.) (a) every common divisor of a and b divides gcd(a, b). (b) if a | bc and gcd(a, b) = 1, then a | c.

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so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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b

step-by-step explanation: