Determine the solution of the given quadratic inequality. ( x + 2 ) ( 2 x − 3 ) > 0 \left(x+2\right)\left(2x-3\right)>0 ( x + 2 ) ( 2 x − 3 ) > 0

x < − 2 o r x > 3 2 x<-2\ or\ x>\frac{3}{2} x < − 2 o r x > 2 3

− 2 < x < 3 2 -2<x<\frac{3}{2} − 2 < x < 2 3

Determine the solution of the given quadratic inequality. ( x − 4 ) ( 4 x − 5 ) ≥ 0 \left(x-4\right)\left(4x-5\right)\ge0 ( x − 4 ) ( 4 x − 5 ) ≥ 0

x ≤ 5 4 o r x ≥ 4 x\le\frac{5}{4}\ or\ x\ge4 x ≤ 4 5 o r x ≥ 4

5 4 ≤ x ≤ 4 \frac{5}{4}\le x\le4 4 5 ≤ x ≤ 4

Determine the solution of the given quadratic inequality. ( 5 x − 3 ) ( x + 1 ) < 0 \left(5x-3\right)\left(x+1\right)<0 ( 5 x − 3 ) ( x + 1 ) < 0

− 1 < x < 3 5 -1<x<\frac{3}{5} − 1 < x < 5 3

x < − 1 o r x > 3 5 x<-1\ or\ x>\frac{3}{5} x < − 1 o r x > 5 3

Determine the solution of the given quadratic inequality. ( 3 x − 2 ) ( 2 x − 3 ) ≤ 0 \left(3x-2\right)\left(2x-3\right)\le0 ( 3 x − 2 ) ( 2 x − 3 ) ≤ 0

2 3 ≤ x ≤ 3 2 \frac{2}{3}\le x\le\frac{3}{2} 3 2 ≤ x ≤ 2 3

x ≤ 2 3 o r x ≥ 3 2 x\le\frac{2}{3}\ or\ x\ge\frac{3}{2} x ≤ 3 2 o r x ≥ 2 3

Determine the solution of the given quadratic inequality. ( x + 5 ) ( x − 10 ) > 0 \left(x+5\right)\left(x-10\right)>0 ( x + 5 ) ( x − 1 0 ) > 0

x < − 5 o r x > 10 x<-5\ or\ x>10 x < − 5 o r x > 1 0

− 5 < x < 10 -5<x<10 − 5 < x < 1 0

Determine the solution of the given quadratic inequality. ( x + 11 ) ( 3 x + 11 ) ≥ 0 \left(x+11\right)\left(3x+11\right)\ge0 ( x + 1 1 ) ( 3 x + 1 1 ) ≥ 0

x ≤ − 11 o r x ≥ − 11 3 x\le-11\ or\ x\ge-\frac{11}{3} x ≤ − 1 1 o r x ≥ − 3 1 1

− 11 ≤ x ≤ − 11 3 -11\le x\le-\frac{11}{3} − 1 1 ≤ x ≤ − 3 1 1

Determine the solution of the given quadratic inequality. ( 2 x − 9 ) ( x − 12 ) < 0 \left(2x-9\right)\left(x-12\right)<0 ( 2 x − 9 ) ( x − 1 2 ) < 0

9 2 < x < 12 \frac{9}{2}<x<12 2 9 < x < 1 2

x < 9 2 o r x > 12 x<\frac{9}{2}\ or\ x>12 x < 2 9 o r x > 1 2

Determine the solution of the given quadratic inequality. ( x + 6 ) ( 4 x − 13 ) ≤ 0 \left(x+6\right)\left(4x-13\right)\le0 ( x + 6 ) ( 4 x − 1 3 ) ≤ 0

− 6 ≤ x ≤ 13 4 -6\le x\le\frac{13}{4} − 6 ≤ x ≤ 4 1 3

x ≤ − 6 o r x ≥ 13 4 x\le-6\ or\ x\ge\frac{13}{4} x ≤ − 6 o r x ≥ 4 1 3

Determine the solution of the given quadratic inequality. ( x − 8 ) ( x + 3 ) > 0 \left(x-8\right)\left(x+3\right)>0 ( x − 8 ) ( x + 3 ) > 0

x < − 3 o r x > 8 x<-3\ or\ x>8 x < − 3 o r x > 8

− 3 < x < 8 -3<x<8 − 3 < x < 8

Determine the solution of the given quadratic inequality. ( x − 6 ) ( 4 x + 6 ) ≥ 0 \left(x-6\right)\left(4x+6\right)\ge0 ( x − 6 ) ( 4 x + 6 ) ≥ 0

x ≤ − 3 2 o r x ≥ 6 x\le-\frac{3}{2}\ or\ x\ge6 x ≤ − 2 3 o r x ≥ 6

− 3 2 ≤ x ≤ 6 \frac{-3}{2}\le x\le6 2 − 3 ≤ x ≤ 6

Determine the solution of the given quadratic inequality. ( 3 x − 8 ) ( x + 5 ) < 0 \left(3x-8\right)\left(x+5\right)<0 ( 3 x − 8 ) ( x + 5 ) < 0

− 5 < x < 8 3 -5<x<\frac{8}{3} − 5 < x < 3 8

x < − 5 o r x > 8 3 x<-5\ or\ x>\frac{8}{3} x < − 5 o r x > 3 8

Determine the solution of the given quadratic inequality. ( x + 7 ) ( 2 x − 1 ) ≤ 0 \left(x+7\right)\left(2x-1\right)\le0 ( x + 7 ) ( 2 x − 1 ) ≤ 0

− 7 ≤ x ≤ 1 2 -7\le x\le\frac{1}{2} − 7 ≤ x ≤ 2 1

x ≤ − 7 o r x ≥ 1 2 x\le-7\ or\ x\ge\frac{1}{2} x ≤ − 7 o r x ≥ 2 1

Determine the solution of the given quadratic inequality. ( 5 x − 9 ) ( x − 2 ) > 0 \left(5x-9\right)\left(x-2\right)>0 ( 5 x − 9 ) ( x − 2 ) > 0

x < 9 5 o r x > 2 x<\frac{9}{5}\ or\ x>2 x < 5 9 o r x > 2

9 5 < x < 2 \frac{9}{5}<x<2 5 9 < x < 2

Determine the solution of the given quadratic inequality. ( x − 6 ) ( x + 6 ) ≥ 0 \left(x-6\right)\left(x+6\right)\ge0 ( x − 6 ) ( x + 6 ) ≥ 0

x ≤ − 6 o r x ≥ 6 x\le-6\ or\ x\ge6 x ≤ − 6 o r x ≥ 6

− 6 ≤ x ≤ 6 -6\le x\le6 − 6 ≤ x ≤ 6

Determine the solution of the given quadratic inequality. ( x + 7 ) ( 8 x + 1 ) < 0 \left(x+7\right)\left(8x+1\right)<0 ( x + 7 ) ( 8 x + 1 ) < 0

− 7 < x < − 1 8 -7<x<\frac{-1}{8} − 7 < x < 8 − 1

x < − 7 o r x > − 1 8 x<-7\ or\ x>\frac{-1}{8} x < − 7 o r x > 8 − 1

Determine the solution of the given quadratic inequality. x ( 4 x − 5 ) ≤ 0 x\left(4x-5\right)\le0 x ( 4 x − 5 ) ≤ 0

0 ≤ x ≤ 5 4 0\le x\le\frac{5}{4} 0 ≤ x ≤ 4 5

x ≤ 0 o r x ≥ 5 4 x\le0\ or\ x\ge\frac{5}{4} x ≤ 0 o r x ≥ 4 5

Determine the solution of the given quadratic inequality. ( 6 x + 7 ) ( 4 x + 8 ) > 0 \left(6x+7\right)\left(4x+8\right)>0 ( 6 x + 7 ) ( 4 x + 8 ) > 0

x < − 2 o r x > − 7 6 x<-2\ or\ x>-\frac{7}{6} x < − 2 o r x > − 6 7

− 2 < x < − 7 6 -2<x<-\frac{7}{6} − 2 < x < − 6 7

Determine the solution of the given quadratic inequality. ( 3 x − 9 ) ( x − 10 ) ≥ 0 \left(3x-9\right)\left(x-10\right)\ge0 ( 3 x − 9 ) ( x − 1 0 ) ≥ 0

x ≤ 3 o r x ≥ 10 x\le3\ or\ x\ge10 x ≤ 3 o r x ≥ 1 0

3 ≤ x ≤ 10 3\le x\le10 3 ≤ x ≤ 1 0

Determine the solution of the given quadratic inequality. ( 5 x + 6 ) ( 7 x − 9 ) < 0 \left(5x+6\right)\left(7x-9\right)<0 ( 5 x + 6 ) ( 7 x − 9 ) < 0

− 6 5 < x < 9 7 -\frac{6}{5}<x<\frac{9}{7} − 5 6 < x < 7 9

x < − 6 5 o r x > 9 7 x<-\frac{6}{5}\ or\ x>\frac{9}{7} x < − 5 6 o r x > 7 9

Determine the solution of the given quadratic inequality. x ( 6 x + 3 ) ≤ 0 x\left(6x+3\right)\le0 x ( 6 x + 3 ) ≤ 0

− 1 2 ≤ x ≤ 0 -\frac{1}{2}\le x\le0 − 2 1 ≤ x ≤ 0

x ≤ − 1 2 o r x ≥ 0 x\le\frac{-1}{2}\ or\ x\ge0 x ≤ 2 − 1 o r x ≥ 0

Quadratic Inequalities

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Practice Problem

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Medium

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CCSS

HSA.CED.A.1, HSA.REI.B.4, HSA.APR.B.3

Standards-aligned

Jeffrey Estores

Used 506+ times

FREE Resource

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Determine the solution of the given quadratic inequality.

$\left(x+6\right)\left(4x-13\right)\le0$

$x\le-6\ or\ x\ge\frac{13}{4}$

$-6\le x\le\frac{13}{4}$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Determine the solution of the given quadratic inequality.

$\left(x-8\right)\left(x+3\right)>0$

$x<-3\ or\ x>8$

$-3<x<8$

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Determine the solution of the given quadratic inequality.

$\left(x-6\right)\left(4x+6\right)\ge0$

$x\le-\frac{3}{2}\ or\ x\ge6$

$\frac{-3}{2}\le x\le6$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

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Quadratic Inequalities

20 questions

Determine the solution of the given quadratic inequality. (x+2)(2x−3)>0\left(x+2\right)\left(2x-3\right)>0(x+2)(2x−3)>0

Determine the solution of the given quadratic inequality. (x−4)(4x−5)≥0\left(x-4\right)\left(4x-5\right)\ge0(x−4)(4x−5)≥0

Determine the solution of the given quadratic inequality. (5x−3)(x+1)<0\left(5x-3\right)\left(x+1\right)<0(5x−3)(x+1)<0

Determine the solution of the given quadratic inequality. (3x−2)(2x−3)≤0\left(3x-2\right)\left(2x-3\right)\le0(3x−2)(2x−3)≤0

Determine the solution of the given quadratic inequality. (x+5)(x−10)>0\left(x+5\right)\left(x-10\right)>0(x+5)(x−10)>0

Determine the solution of the given quadratic inequality. (x+11)(3x+11)≥0\left(x+11\right)\left(3x+11\right)\ge0(x+11)(3x+11)≥0

Determine the solution of the given quadratic inequality. (2x−9)(x−12)<0\left(2x-9\right)\left(x-12\right)<0(2x−9)(x−12)<0

Determine the solution of the given quadratic inequality. (x+6)(4x−13)≤0\left(x+6\right)\left(4x-13\right)\le0(x+6)(4x−13)≤0

Determine the solution of the given quadratic inequality. (x−8)(x+3)>0\left(x-8\right)\left(x+3\right)>0(x−8)(x+3)>0

Determine the solution of the given quadratic inequality. (x−6)(4x+6)≥0\left(x-6\right)\left(4x+6\right)\ge0(x−6)(4x+6)≥0

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Discover more resources for Mathematics

Determine the solution of the given quadratic inequality.

$\left(x+2\right)\left(2x-3\right)>0$

Determine the solution of the given quadratic inequality.

$\left(x-4\right)\left(4x-5\right)\ge0$

Determine the solution of the given quadratic inequality.

$\left(5x-3\right)\left(x+1\right)<0$

Determine the solution of the given quadratic inequality.

$\left(3x-2\right)\left(2x-3\right)\le0$

Determine the solution of the given quadratic inequality.

$\left(x+5\right)\left(x-10\right)>0$

Determine the solution of the given quadratic inequality.

$\left(x+11\right)\left(3x+11\right)\ge0$

Determine the solution of the given quadratic inequality.

$\left(2x-9\right)\left(x-12\right)<0$

Determine the solution of the given quadratic inequality.

$\left(x+6\right)\left(4x-13\right)\le0$

Determine the solution of the given quadratic inequality.

$\left(x-8\right)\left(x+3\right)>0$

Determine the solution of the given quadratic inequality.

$\left(x-6\right)\left(4x+6\right)\ge0$