Question

Solve the inequality for u.
-3u-14>3u+16

Answer 1

Hi student, let me help you out!

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First of all, we need to solve this inequality for u. We can easily do it if we follow these steps:

1. Subtract 3u from both sides.
2. Add 14 to both sides.
3. Solve for u.

Step 1. Subtract 3u from both sides:
`\mathrm{-3u-3u-14 < 16}`.

Upon simplifying, we get
`\mathrm{-6u-14 < 16}`.

Step 2. Add 14 to both sides:
`\mathrm{-6u < 16+14}`

Upon simplifying, we get
`\mathrm{-6u < 30}`

Step 3. Solve for u, which can be done by dividing both sides by -6:

`\mathrm{-6u/(-6)=30/{-6)}}`.

Upon simplifying, we get
`\mathrm{u > -5}`.

Have you noticed that the sign of the inequality changed from "less than" to "greater than"? This happens every time we multiply, or divide, both sides of an inequality by a negative number. The sign changes from less than to greater than, or the other way around.

Thus, the solution is
`\bigstar\underline{\boxed{\mathrm{u > -5}}}`

Hope it helped you out, ask in comments if any queries arise.