2.15 Solving inequalities Quiz

1. Solve $x^{2}-x-6\le0$.

• A. $-2\le x\le3$
• B. $x\le-2$ or $x\ge3$
• C. $-3\le x\le2$
• D. $-2<x<3$

2. Solve $x(x-2)(x+4)<0$.

• A. $x<-4$ or $0<x<2$
• B. $-4<x<0$ or $x>2$
• C. $-4<x<2$
• D. $0<x<2$

3. Which method is valid for $\frac{3}{x-1}<2$?

• A. Multiply both sides by $x-1$
• B. Multiply both sides by $(x-1)^{2}$
• C. Take reciprocals of both sides
• D. Square both sides

4. Solve $\frac{x+2}{x-1}\ge0$.

• A. $x\le-2$ or $x>1$
• B. $x\le-2$ or $x\ge1$
• C. $-2\le x<1$
• D. $x>1$

5. The graphs of $y=g(x)$ and $y=f(x)$ meet only at $x=1$ and $x=5$, and $g(3)>f(3)$ with both functions continuous. Which is certainly true?

• A. $g(x)>f(x)$ for $1<x<5$
• B. $g(x)>f(x)$ for all $x$
• C. $g(x)<f(x)$ for $1<x<5$
• D. $g(x)=f(x)$ for $1<x<5$