Algebraic and modulus inequalities Quiz

1. Solve $x^2-5x+6<0$.

• A. $2<x<3$
• B. $x<2$ or $x>3$
• C. $x<3$
• D. $x>2$

2. Why can you not multiply both sides of $\frac{3}{x-2}>1$ by $x-2$ and keep the inequality sign?

• A. The inequality sign would never change.
• B. $x-2$ is always positive.
• C. $x-2$ may be negative, which would reverse the sign.
• D. It would make the right-hand side zero.

3. Solve $|x-4|<3$.

• A. $x<7$
• B. $1<x<7$
• C. $x<1$ or $x>7$
• D. $x>1$

4. Solve $|2x+1|>5$.

• A. $-3<x<2$
• B. $x>2$
• C. $x<-3$
• D. $x<-3$ or $x>2$

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

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