One-Variable Non-Linear Inequality Problem-Solving

A solution to the system of inequalities:           y < -1/2x + 3 and y < (x+1)² is : 

• (0, 6) 
• (-1, 4)
• (2, 1)
• (3, 4)

All are solutions to the given inequalities           { y <-1/2(x-1)²+5 and -5 <y - x   } EXCEPT:

• (0, 0)
• (10, 1)
• (-2, -3)
• (1, 2)

Identify the solutions to the system of inequalities. Select all that apply.

• (0, 0)

• (4, 0)

• (0, 4)

• (-2, 0)

Identify the solutions to the system of quadratic inequalities. Select all that apply.

• {(0, 1)}

• {(1, 0)}

• {(-1, 0)}

• {(0, -1)}

6x² - 54 ≤ 0

• -3 ≤ x ≤ 3
• x ≤ -3 or x ≥ 3
• -3 < x < 3
• x < -3 or x > 3

8x + 140 > 4x^{2
hint: put squared term on the LEFT!}

• -5 < x < 7
• -3 ≤ x ≤ 12
• 4 < x < 15
• -2 < x < 10

x² - 9x - 112 ≥ 0

• -7 < x < 16
• -7 ≤ x ≤ 16
• x < -7 or x > 16
• x ≤ -7 or x ≥ 16

-3x² + 45 ≥ 6x

• -5 < x < 3
• -5 ≤ x ≤ 3
• x < -5 or x > 3
• x ≤ -5 or x ≥ 3

-8x² - 9 ≥ 0

• no solution
• all reals
• x = 1.125
• x ≠ 1.125

4x² - 8x < 77

• -3.5 < x < 5.5
• -2.5 < x < 7.5
• -4 < x < 8
• -6 < x < 8