Solving multi-step problems using non-linear inequalities in one variable

Given an inequality has ONE radical sign, which of the following must you always do FIRST?

• flip the inequality symbol

• square or cube both sides

• divide everything by -1

• isolate the radical symbol

Solve the inequality.
 $5-\sqrt{b-7}\ge10$  

• No solution

•  $7\le x\le32$  

•  $7\le x$  

•  $x\le32$  

Solve the inequality

 $4-\sqrt{x+2}>3$  

•  $-2\le x<-1$  

•  $-2<x<-1$  

•  $x>-1$  

•  $x<-1$  

Graph the solution set of the radical inequality on a number line: √(8x - 9) ≤ 1

• x > 5/4

• x ≥ 5/4

• x ≤ 5/4

• x ≤ 9/8

Graph the solution set of the radical inequality on a number line: √(6x + 7) < 2

• x < -3/9 or x > 1/3 is the only solution

• x < -3/9 and x > 1/3

• x < -3/9 or x > 1/3

• x < -3/9 or x > 1/3 or x = 0

Solve the following radical inequality algebraically: √(7x + 8) ≥ 9

• x ≥ 73/7

• x ≥ 8

• x ≤ 9

• x ≤ 73/7

√(3x-2 )> 13

• [⅔, 57)
• (57, +∞)
• (-∞, ⅔)
• [57, + ∞)