Name: Randall Who is asking: Teacher Level: Secondary Question: I don't seem to be able to solve this: | n + 4 | + | 3 - 2n | = 16 Can you help? Hi Randall, I think that the most straightforward way to approach this problem is with a case argument. The cases come from the fact that if a is non-negative then | a | = a and if a is negative then | a | = - a There are four cases, depending on the sign of n + 4 and 3 - 2n. Case 1: n + 4 >= 0 and 3 - 2n >= 0 | n + 4 | + | 3 - 2n | = 16 n + 4 + 3 - 2n = 16 n = - 9 Check: | -9 + 4 | + | 3 -2(-9) | = 5 + 21 = 26 which is not 16. Hence n = -9 is not a solution. Case 2: n + 4 >= 0 and 3 - 2n < 0 | n + 4 | + | 3 - 2n | = 16 n + 4 - 3 + 2n = 16 3n = 15 n = 5 Check: | 5 + 4 | + | 3 -2(5) | = 9 + 7 = 16. Hence n = 5 is a solution. Case 3: n + 4 < 0 and 3 - 2n >= 0 | n + 4 | + | 3 - 2n | = 16 - n - 4 + 3 - 2n = 16 -3 n = 17 n =  -17/3 Check: |  -17/3 + 4 | + | 3 -2(  -17/3) | = 5/3 + 43/3 = 16. Hence n =  -17/3 is a solution. Case 4: n + 4 < 0 and 3 - 2n < 0 | n + 4 | + | 3 - 2n | = 16 - n - 4 - 3 + 2n = 16 n = 23 Check: | 23 + 4 | + | 3 -2(23) | = 27 + 43 = 70 which is not 16. Hence n = 23 is a solution. Thus there are two solutions, n = 5 and n =  -17/3 Cheers, Penny Go to Math Central