6
algebra

A rectangle has a length of x+5x + 5 and a width of 4. If the area must be at least 40, which inequality represents the possible values of xx?

A

x5x \geq 5

B

x5x \leq 5

C

x10x \geq 10

D

x35x \geq 35

Correct Answer: A

Choice A is the correct answer. Area = Length ×\times Width.

  1. Area Formula: 4(x+5)4(x + 5)
  2. Constraint: At least 40 40\rightarrow \geq 40
  3. Inequality: 4(x+5)404(x + 5) \geq 40
  4. Divide by 4: x+510x + 5 \geq 10
  5. Subtract 5: x5x \geq 5

?�� Strategic Tip: You can also distribute first: 4x+20404x20x54x + 20 \geq 40 \rightarrow 4x \geq 20 \rightarrow x \geq 5.

Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it forgets to subtract 5. Choice D is incorrect because it subtracts 5 from 40 directly without dividing by 4.