Solve the rational inequality and state your solution in interval notation. 3 x − 7 x + 2 > 0 \frac{3x-7}{x+2}>0 x + 2 3 x − 7 > 0

( − ∞ , − 2 ) ∪ ( 7 3 , + ∞ ) \left(-\infty,-2\right)\cup\left(\frac{7}{3},\ +\infty\right) ( − ∞ , − 2 ) ∪ ( 3 7 , + ∞ )

( − 2 , 7 3 ) \left(-2,\ \frac{7}{3}\right) ( − 2 , 3 7 )

( 7 3 , + ∞ ) \left(\ \frac{7}{3},\ +\infty\right) ( 3 7 , + ∞ )

( − ∞ , − 2 ) ∪ [ 7 3 , + ∞ ) \left(-\infty,-2\right)\cup\left[\frac{7}{3},\ +\infty\right) ( − ∞ , − 2 ) ∪ [ 3 7 , + ∞ )

Solve the rational inequality and state your solution in interval notation. − x x − 3 ≥ 0 \frac{-x}{x-3}\ge0 x − 3 − x ≥ 0

[ 0 , 3 ) \left[0,\ 3\right) [ 0 , 3 )

( 0 , + ∞ ) \left(0,\ +\infty\right) ( 0 , + ∞ )

( − ∞ , 0 ) ∪ ( 3 , + ∞ ) \left(-\infty,\ 0\right)\cup\left(3,\ +\infty\right) ( − ∞ , 0 ) ∪ ( 3 , + ∞ )

( − ∞ , 0 ] ∪ [ 3 , + ∞ ) \left(-\infty,\ 0\right]\cup\left[3,\ +\infty\right) ( − ∞ , 0 ] ∪ [ 3 , + ∞ )

Solve the inequality 5 3 x − 3 4 x > 5 6 \frac{5}{3x}-\frac{3}{4x}>\frac{5}{6} 3 x 5 − 4 x 3 > 6 5

0 < x < 1.1 0<x<1.1 0 < x < 1 . 1

x < 0 o r x > 1.1 x<0\ or\ x>1.1 x < 0 o r x > 1 . 1

Solve the inequality 3 4 − 1 x − 3 > x x + 4 \frac{3}{4}-\frac{1}{x-3}>\frac{x}{x+4} 4 3 − x − 3 1 > x + 4 x

− 4 < x < 3 -4<x<3 − 4 < x < 3

x < − 4 o r x > 3 x<-4\ or\ x>3 x < − 4 o r x > 3

Solve the inequality x − 2 x + 4 > x + 1 x + 10 \frac{x-2}{x+4}>\frac{x+1}{x+10} x + 4 x − 2 > x + 1 0 x + 1

− 10 < x < − 4 o r x > 8 -10<x<-4\ \ \ or\ \ \ x>8 − 1 0 < x < − 4 o r x > 8

x < − 4 o r x > 8 x<-4\ \ or\ \ \ x>8 x < − 4 o r x > 8

− 10 < x < − 4 -10<x<-4 − 1 0 < x < − 4

Quadratic Inequalities

Authored by Hasan Gun

English, Education, Mathematics

9th - 12th Grade

CCSS covered

Used 18+ times

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Which of the following is the solution set of $x^2-9x-112\ge0$ ?

{x l -7 < x < 16}

{x l -7 ≤ x ≤ 16}

{x l x < -7 or x > 16}

{x l x ≤ -7 or x ≥ 16}

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Quadratic Inequalities

Solve: 5x - 10x2 < 0

Solve:3x - x2 > 0

5x2 + 10x + 7 ≥ 0

6x2 - 54 ≤ 0

-3x2 + 6x - 3 > 0

-3x2 + 6x - 3 > 0

-8x2 - 9 ≥ 0

Solve the quadratic inequality: x2+11x+10≥0x^2+11x+10\ge0x2+11x+10≥0

Solve the quadratic inequality: x2+10x+16<0x^2+10x+16<0x2+10x+16<0

Which of the following is the solution set of x2−9x−112≥0x^2-9x-112\ge0x2−9x−112≥0 ?

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Solve: 5x - 10x² < 0

Solve:
3x - x²> 0

5x² + 10x + 7 ≥ 0

6x² - 54 ≤ 0

-3x² + 6x - 3 > 0

-3x² + 6x - 3 > 0

-8x² - 9 ≥ 0

Solve the quadratic inequality:

$x^2+11x+10\ge0$

Solve the quadratic inequality:

$x^2+10x+16<0$

Which of the following is the solution set of $x^2-9x-112\ge0$ ?