let

b = the money invested in bonds

c = the money invested in CD

A total amount of 83,000 is to be invested, some in bonds and some in CDs:

b + c = 83,000

b = 83,000 - c

The amount invested in bonds is to exceed that in CDs by 8,000:

b > c + 8000

plug b = 83,000 - c into the last inequality:

83,000 - c >= c + 8000

by solving we find

c <= $37,500

click here to see the step by step solution of the inequality

b >= 83,000 - 37,500

b > $45,500

not more than $37,500 will be invested in CDs and not less than $45,500 in bonds.