Non-linear inequalities (one variable)

Solve the following radical inequality algebraically: √(9x + 10) > 11

• x > 11

• x = 12.3333

• x < 12.3333

• x > 12.3333

For a square root inequality equation, you must first​ (a)   and then solve ​ (b)   equations: one of them is the original equation, and the other is the part under the radical set greater than or equal to ​ (c)   .

• isolate the radical
• two
• zero
• three
• square both sides

 $\sqrt{2x+8}-3\ <\ 2$  

Solve:

• (- $\infty$  , 4.5)

• [-4, $\infty$  )

• [-4, 4.5)

• (-4, 4.5)

3 + √(3x+12) ≤ 9

• [-4,8]
• (- ∞, 8]
• [-4,-2]
• [4,6]

Solve Radical Inequality
 $\sqrt{3x+1}>\sqrt{4x-2}$  

•  $\frac{1}{2}\le x<3$  

•  $x\ge\frac{1}{2}$  

•  $-\frac{1}{3}\le x<3$  

•  $-\frac{1}{3}\le x\le\frac{1}{2}$  

Given the inequality $\sqrt{x-1}<5$  , why is the solution NOT (-∞,26) ?

• because 5 is not a perfect square

• because 5+1 = 6 and not 26

• because the radicand must be greater than 0 and therefore x must be greater than 1

• [-4,8]

• (- ∞, 8]

• [-4,-2]

• [4,8]

solve:   $\sqrt{8x-16}\ge4$  

• [2,4]

• [2, ∞)

• [4,∞)

• [-2,4]

• (-∞,3]

• (-8, 17]

• [-8, 17)

• [-8, 17]

• [-8, -3]

• [6,∞)

• (-∞,22)

• [6, 22)

• (22, ∞)

• [6,10]