Question

What is the first step when solving the following inequality x+2/-5<4? Group of answer choices A. Add 5 to both sides and DO NOT flip the inequality sign. B. Multiply both sides by -5 and DO NOT flip the inequality sign. C. Multiply both sides by -5 and flip the inequality sign. D. Subtract 2 from both sides and flip the inequality sign.

Answer 1

Assuming we're dealing with $\frac{x+2}{-5} < 4$, which is the same as writing (x+2)/(-5) < 4, then the answer is choice C.

We multiply both sides by -5 and this will flip the inequality sign.

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Multiplying or dividing both sides by a negative number flips the inequality sign.

An example would be saying -2x < 10 leads to x > -5

What we can do is divide both sides by -2 and flip the inequality sign, or we could follow the steps shown below

• -2x < 10
• 0 < 10+2x ... adding 2x to both sides
• -10 < 2x ... subtracting 10 from both sides; this is one way to see why the sign flip happens
• 2x > -10
• x > -10/2 ..... dividing both sides by 2
• x > -5