Question

Which of the following inequalities have the same solution set? Select all that apply (>= means greater than or equal to and <= means less than or equal to) *

0 points
7n + 4 - 5n <= 2(n+2)
7 + 6a >= -4(2-a) -2a
2(x+4) - 4x>= -8
7-6a>= -6a -7
-3(n-4) >= 10-3n

Answer 1

7n + 4 - 5n <= 2(n+2) Let's simplify these expression first 2n + 4 <= 2(n + 2) 2(n +4) = 2n + 4 The LHS and RHS expressions are the same but the inequality says contrary Hence 2n + 4 is not less than but equal to 2(n + 2). 7+ 6a >= -4(2-a) - 2a -4(2-a) - 2a = -8 + 4a - 2a = -8 + 2a. It should be obvious that 7 +6a is greater than the RHS expression. Suppose a= 2 then we have 7 + 6(2) = 19 while -8 + 2(2) = - 8 + 4 = -4 So it follows that 7 + 6a >= -4(2-4) -2a 4x >= 8. The expression is always true so the equal to option is out.