8

Set 5: Linear Inequalities (Intermediate)

Explanation

Answer: C

Solve: 5x32+4<9\frac{5x - 3}{2} + 4 < 9

A.

x<1x < 1

B.

x>1x > 1

C.

x<2.6x < 2.6

✓ Correct
D.

x>2.6x > 2.6

Detailed Explanation

Choice C is correct. Choice C is the correct answer. Clear the fraction first, then solve systematically. 1. Subtract 4: 5x32<5\frac{5 x-3}{2} < 5 2. Multiply by 2: 5x3<105x - 3 < 10 3. Add 3: 5x<135x < 13 4. Divide by 5: x<135=2.6x < \frac{13}{5} = 2.6 Strategic Tip: Multiplying both sides by a positive number (like 2) doesn't change inequality direction. Choice A is incorrect because it likely comes from incorrect arithmetic when combining constants. Choice B is incorrect because it reverses the direction without justification. Choice D is incorrect because it combines wrong direction with the correct value.

Key Steps:

The correct answer is x<2.6x < 2.6

Why others are wrong:
A: Choice A is incorrect and may result from a calculation error.
B: Choice B is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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