14 3 < x < 17 3 \frac{14}{3}\ <\ x\ <\ \frac{17}{3} 3 1 4 < x < 3 1 7

3 14 < x < 3 17 \frac{3}{14}\ <\ x\ <\ \frac{3}{17} 1 4 3 < x < 1 7 3

4 < x < 3 4\ <\ x\ <3 4 < x < 3

42 < x < 51 42\ <\ x\ <\ 51 4 2 < x < 5 1

− 10 ≤ 4 x − 5 2 < 20 -10\le\frac{4x-5}{2}<20 − 1 0 ≤ 2 4 x − 5 < 2 0

− 3 3 4 ≤ x < 11 1 4 -3\ \frac{3}{4}\le x<11\ \frac{1}{4} − 3 4 3 ≤ x < 1 1 4 1

3 3 4 ≤ x < 11 1 4 3\ \frac{3}{4}\le x<11\ \frac{1}{4} 3 4 3 ≤ x < 1 1 4 1

− 3 3 4 > x ≥ 11 1 4 -3\ \frac{3}{4}>x\ge11\ \frac{1}{4} − 3 4 3 > x ≥ 1 1 4 1

3 3 4 ≥ x > − 11 1 4 3\ \frac{3}{4}\ge x>-11\ \frac{1}{4} 3 4 3 ≥ x > − 1 1 4 1

− 2 ( x − 1 ) ≥ 10 o r 4 ( x + 2 ) ≥ 20 -2\left(x-1\right)\ge10\ or\ 4\left(x+2\right)\ge20 − 2 ( x − 1 ) ≥ 1 0 o r 4 ( x + 2 ) ≥ 2 0

x ≤ − 4 o r x ≥ 3 x\le-4\ or\ x\ge3 x ≤ − 4 o r x ≥ 3

x ≤ 4 o r x ≥ − 3 x\le4\ or\ x\ge-3 x ≤ 4 o r x ≥ − 3

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

x ≥ − 4 o r x ≥ 3 x\ge-4\ or\ x\ge3 x ≥ − 4 o r x ≥ 3

Write a compound inequality for the following situation. Water will not be in liquid form when it is colder than 32ºF or warmer than 212ºF.

32 ≤ t ≤ 212 32\le t\le212 3 2 ≤ t ≤ 2 1 2

32 ≥ t ≥ 212 32\ge t\ge212 3 2 ≥ t ≥ 2 1 2

t ≤ 32 o r t ≥ 212 t\le32\ or\ t\ge212 t ≤ 3 2 o r t ≥ 2 1 2

t ≤ − 32 o r t ≥ 212 t\le-32\ or\ t\ge212 t ≤ − 3 2 o r t ≥ 2 1 2

Write a compound inequality for the following situation. The width of a parking space needs to be at least 8 ft and no more than 11 feet.

8 ≤ w ≤ 11 8\le w\le11 8 ≤ w ≤ 1 1

w ≤ 8 o r w ≥ 11 w\le8\ or\ w\ge11 w ≤ 8 o r w ≥ 1 1

8 ≥ w ≥ 11 8\ge w\ge11 8 ≥ w ≥ 1 1

w > 8 o r w > 11 w>8\ or\ w>11 w > 8 o r w > 1 1

The force exerted on a spring is proportional to the distance the spring stretches from its relaxed position. Suppose you stretch a spring distance d in inches by applying force F in pounds. For a certain spring, d/F = 0.6 . You apply forces between 30 and 50 pounds, inclusive. Which inequality describes the stretch of the spring?

18 ≤ d ≤ 30 18\le d\le30 1 8 ≤ d ≤ 3 0

d ≤ 18 o r d ≥ 30 d\le18\ or\ d\ge30 d ≤ 1 8 o r d ≥ 3 0

50 ≤ d ≤ 83.3 50\le d\le83.3 5 0 ≤ d ≤ 8 3 . 3

18 < d < 30 18<d<30 1 8 < d < 3 0

The acidity of water in a swimming pool is considered normal if the average pH reading is between 7.5 and 7.9 inclusive. The first two readings for a swimming pool are 7.6 and 8.1. What possible values for the third reading p will make the average pH normal?

The value for the third reading must be between 6.8 and 8.0, inclusive.

The value for the third reading must be between 6.5 and 7.8, inclusive.

The value for the third reading must be between 6.9 and 8.1, inclusive.

The value for the third reading must be between 6.7 and 8.2, inclusive.

When a person exercises, the pulse rate rises. Recommended pulse rates vary with age and physical condition. For vigorous exercise, such as jogging, the inequality gives a target range for pulse rate R, based on a age a. 0.7 ( 220 − a ) ≤ R ≤ 0.85 ( 220 − a ) 0.7\left(220-a\right)\le R\le0.85\left(220-a\right) 0 . 7 ( 2 2 0 − a ) ≤ R ≤ 0 . 8 5 ( 2 2 0 − a ) What is the target range for pulse rates for a person 35 years old?Round to the nearest whole number.

130 ≤ R ≤ 157 130\le R\le157 1 3 0 ≤ R ≤ 1 5 7

132 ≤ R ≤ 159 132\le R\le159 1 3 2 ≤ R ≤ 1 5 9

128 ≤ R ≤ 155 128\le R\le155 1 2 8 ≤ R ≤ 1 5 5

134 ≤ R ≤ 159 134\le R\le159 1 3 4 ≤ R ≤ 1 5 9

Solve − 2 ≤ d + 1 2 < 4 1 2 -2\le d\ +\ \frac{1}{2}<4\ \frac{1}{2} − 2 ≤ d + 2 1 < 4 2 1

− 2 1 2 ≤ d < 4 -2\frac{1}{2}\le d<4 − 2 2 1 ≤ d < 4

2 1 2 ≤ d < 4 2\frac{1}{2}\le d<4 2 2 1 ≤ d < 4

− 2 1 2 < d ≤ 4 -2\frac{1}{2}<d\le4 − 2 2 1 < d ≤ 4

− 1 1 2 ≤ d < 4 -1\frac{1}{2}\le d<4 − 1 2 1 ≤ d < 4

Solve − 2 ≤ 5 − x 3 ≤ 2 -2\le\frac{5-x}{3}\le2 − 2 ≤ 3 5 − x ≤ 2

− 1 ≤ x ≤ 11 -1\le x\le11 − 1 ≤ x ≤ 1 1

1 < x ≤ 10 1<x\le10 1 < x ≤ 1 0

− 1 < x < 11 -1<x<11 − 1 < x < 1 1

1 ≤ x ≤ 11 1\le x\le11 1 ≤ x ≤ 1 1

SOLVE COMPOUND INEQUALITIES

Authored by Francisco Artuz

Mathematics

9th Grade

CCSS covered

Used 41+ times

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MULTIPLE CHOICE QUESTION

15 mins • 1 pt

-2 < x - 9 < 3

x < 12

7 < x

7 < x < 12

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.3

CCSS.HSA.REI.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve: -3 ≤ 2x - 1 ≤ 5

-1 ≤ x ≤ 3

-1 < x < 3

1 < x < 3

1 ≤ x ≤ 3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.3

MULTIPLE CHOICE QUESTION

15 mins • 12 pts

0 < x + 7 < 9

-7<x and x<2

-7<x or x<2

-7>x and x>2

-7>x or x>2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Write an inequality for Graph 3.

x ≤ -2 AND x > 5

x ≤ -2 OR x > 5

x ≥ -2 OR x < 5

-2 ≤ x < 5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

−6 < 2t − 5 < 3

−0.5 < t < 1

0.5 < t < −1

−11/2 < t < 2

11/2 < t < −2

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

2 < 3x - 12 < 5

$\frac{14}{3}\ <\ x\ <\ \frac{17}{3}$

$\frac{3}{14}\ <\ x\ <\ \frac{3}{17}$

$4\ <\ x\ <3$

$42\ <\ x\ <\ 51$

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

CCSS.HSA.REI.A.1

MULTIPLE CHOICE QUESTION

15 mins • 1 pt

Solve:
3x + 2 < -4 or 4x + 4 > 28

x < -2 or x > 6

x < 2 or x > 6

x < -2 and x > 6

x < 2 and x > 6

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

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SOLVE COMPOUND INEQUALITIES

-2 < x - 9 < 3

Solve: -3 ≤ 2x - 1 ≤ 5

0 < x + 7 < 9

Write an inequality for Graph 3.

−6 < 2t − 5 < 3

2 < 3x - 12 < 5

Solve: 3x + 2 < -4 or 4x + 4 > 28

Solve: 3x + 2 < -4 or 4x + 4 > 28

Solve: 6x + 2 < -16 or -4x + 5 < 1

Write an inequality for Graph 3.

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Solve:
3x + 2 < -4 or 4x + 4 > 28

Solve:
3x + 2 < -4 or 4x + 4 > 28

Solve:
6x + 2 < -16 or -4x + 5 < 1