9
algebra

If 1.5x+2.40.9x+61.5x + 2.4 \leq 0.9x + 6, what is the solution?

A

x6x \leq 6

B

x6x \geq 6

C

x4x \leq 4

D

x4x \geq 4

Correct Answer: A

Choice A is the correct answer. Decimals follow the same rules as whole numbers.

  1. Subtract 0.9x: 1.5x0.9x+2.461.5x - 0.9x + 2.4 \leq 6, giving 0.6x+2.460.6x + 2.4 \leq 6
  2. Subtract 2.4: 0.6x3.60.6x \leq 3.6
  3. Divide by 0.6: x6x \leq 6

?�� Strategic Tip: Alternatively, multiply everything by 10 to eliminate decimals: 15x+249x+6015x + 24 \leq 9x + 60.

Choice B is incorrect because it reverses the direction without cause. Choice C is incorrect because it might come from dividing 2.4 by 0.6 without subtracting first. Choice D is incorrect because it combines wrong value and wrong direction.