Question 1045663
The limit of the function from the left of x = -2 should be equal to the limit of the function from the right of x = -2.  
Upon substitution these give

-2 + 2p = 3p*-2+q <===> -2 + 2p = -6p + q <===> q = 8p - 2  <---Equation A

Similarly, The limit of the function from the left of x = 1 should be equal to the limit of the function from the right of x = 1.  
Upon substitution these give

3p +q = 3-2q  <===>  3p + 3q = 3  <===>  p + q = 1  <---Equation B

After substituting Equation A into Equation B, we get

p + 8p - 2 = 1  ===> 9p = 3  ===> {{{highlight(p = 1/3)}}}, and hence {{{highlight(q = 2/3)}}}.