9
algebra

If 0.5x1.20.3x+0.80.5x - 1.2 \leq 0.3x + 0.8, what is the solution?

A

x10x \leq 10

B

x10x \geq 10

C

x4x \leq 4

D

x4x \geq 4

Correct Answer: A

Choice A is the correct answer. Decimals in inequalities work the same as whole numbers.

  1. Subtract 0.3x: 0.5x0.3x1.20.3x0.3x+0.80.5x - 0.3x - 1.2 \leq 0.3x - 0.3x + 0.8, giving 0.2x1.20.80.2x - 1.2 \leq 0.8
  2. Add 1.2: 0.2x2.00.2x \leq 2.0
  3. Divide by 0.2: x10x \leq 10

?�� Strategic Tip: You can multiply all terms by 10 to eliminate decimals: 5x123x+85x - 12 \leq 3x + 8, then solve normally.

Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it might come from dividing 0.8 by 0.2 without adding 1.2 first. Choice D is incorrect because it combines wrong value with wrong direction.