Solve an inequality. Suspect the book's answer is wrong.

[Nibin]

Hi. I've gone over this exercise from Schaum's Calculus 3 times and I suspect the answer the give is wrong (seems to happen a lot). I'd be grateful if someone can quickly go over my working out, just to confirm I'm not making a stupid mistake. Thanks

Picture of book has the original question and given answer marked in pencil. The other photo is of my working out of the problem.

 

[mmm4444bot]

I'd be grateful if someone can quickly go over my working out, just to confirm I'm not making a stupid mistake.

It looks like you're both wrong. :cool:

Your work looks great, but the signs in your chart for -3x-10 are transposed about the x-intercept.

y = -3x - 10

This line has negative slope, and it crosses the x-axis at -10/3. Therefore, y must be positive to the left of the intercept, and negative to the right. Fix that, and you'll be in good shape.

(You wrote a zero directly below -10/3 on your sign chart; I'm not sure what that means.)

The book's answer contains a sign error. I'm familiar with their work; they ought to hire some proofreaders.

PS: Don't think of your mistake as stupid; instead, consider it a chance to grow your brain. Once you understand a mistake, fix it, and move forward, your brain will strengthen some of its connections, to reduce the probability that you make the same error in the future.