Inequalities

Solve

 $x+1\le1$  .

•  $x=0$  

•  $x<0$  

•  $x\le0$  

•  $x\ge0$  

Solve

 $2x-1>6$  

•  $x>\frac{5}{2}$  

•  $x>-\frac{5}{2}$  

•  $x<\frac{7}{2}$  

•  $x>\frac{7}{2}$  

Solve

 $1-2x\ge5$  

•  $x\ge3$  

•  $x\le3$  

•  $x\le-2$  

•  $x\ge-2$  

Solve

 $2\le x-1<6$  

•  $3\le x\le7$  

•  $3<x<7$  

•  $3<x\le7$  

•  $3\le x<7$  

Solve

 $2x<x+1\le1-x$  

•  $0\le x<1$  

•  $0<x\le1$  

•  $x\le0$  

•  $x\le1$  

Solve

 $1+x\le2x<3\left(x+1\right)$  

•  $-3<x\le1$  

•  $-3<x\ge1$  

•  $x>1$  

•  $x\ge1$  

Given a is a constant, which of the following is equivalent to

 $\left|x+a\right|<2$  

•  $x+a<2$  

•  $x+a<2\ \ or\ \ x+a<-2$  

•  $x+a<2\ \ \ and\ \ x+a<-2$  

•  $-2<x+a<2$  

Solve

 $\left|x-3\right|\le5$  

•  $x\le8$  

•  $x\ge-2$  

•  $-2\le x<8$  

•  $-2\le x\le8$  

There are 5-steps in solving a non-linear inequality, which of the following is the correct sequence?

P: Critical Values

Q: Solving Method (Number line method/Table sign method)

R: Rewrite the inequalities so that RHS is 0

S: Solution

T: Linear factor(s) of the variable/unknown

• R, Q, P, T, S

• R, P, T, Q, S

• R, T, P, Q, S

• R, P, T, Q, S

The figure shows the steps to solve a rational inequality

 $\frac{x-8}{x-2}\le0$ . What is the solution of the inequality? 

•  $x<2$  

•  $x\le8$  

•  $2\le x\le8$  

•  $2<x\le8$