Question

Choose the solution to this inequality.

9
1/2 ≥b + 2/1/2
O
10
O
A. b2²/
B. b≤11/100
O C. bs-²/
O D.
D. b < 2 ²1/1

Answer 1

`\text{Choice C: }\boxed{b\le 1 (7)/(10)\\\\}`

Explanation:

We are given inequality:

`(7)/(2)\ge \:b\:+\:(9)/(5)`

• Switch sides:
  
  `b+(9)/(5)\le (7)/(2)`
  
• Move
  `(9)/(5)` to the right side(sign switches to negative)
  
  `b \le (7)/(2) - (9)/(5)\\\\`
  
• Adjust the fractions on the right side so they end up with the same denominator which is the LCM of 2 and 5 = 10
  
  `(7)/(2)=(7\cdot \:5)/(2\cdot \:5)=(35)/(10)\\\\\\(9)/(5)=(9\cdot \:2)/(5\cdot \:2)=(18)/(10)\\\\\\\\(35)/(10)-(18)/(10)\\\\\\= (17)/(10)\\\\`
  
• So the original inequality becomes:
  
  `b\le (17)/(10)`
  
• 17/10 = 1 7/10
  
• Answer is:
  
  `b\le 1 (7)/(10)\\\\`
  which is choice C