Algebraic inequalities Quiz

1. Solve $\frac{x+5}{x+2}>0$.

• A. $-5<x<-2$
• B. $x<-5$ or $x>-2$
• C. $x>-2$
• D. $x<-2$

2. Which step is valid for $\frac{2}{x-1}>\frac{3}{x+4}$?

• A. Multiply both sides by $(x-1)(x+4)$ without further thought.
• B. Multiply both sides by $(x-1)^2(x+4)^2$.
• C. Cross-multiply to get $2(x+4)>3(x-1)$ always.
• D. Take reciprocals and keep the sign.

3. Solve $|x-3|<2$.

• A. $x<1$ or $x>5$
• B. $-2<x<2$
• C. $1<x<5$
• D. $x>5$

4. Which values of $x$ can possibly satisfy $|x^2-1|<x-3$?

• A. Only $x>3$
• B. Only $x<3$
• C. All real $x$
• D. Only $x<-1$

5. Solve $(x-1)^2(x-4)\le0$.

• A. $x\ge4$
• B. $1\le x\le4$
• C. $x\le1$ or $x\ge4$
• D. $x\le4$