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Solving Compound Sentences with Inequalities Worksheet

Solving Compound Sentences with Inequalities Worksheet
  • Page 1
 1.  
Solve and graph the compound inequality.
13x > 39 and 12x < - 24


a.
Graph 2
b.
Graph 1
c.
no solution
d.
Graph 3


Solution:

13x > 39 and 12x < - 24

x > 3 and x < - 2

There are no values for x that are both greater than 3 and less than - 2.

The compound inequality has no solution.


Correct answer : (3)
 2.  
Choose the graph which is the solution set of the conjunction 2 + x >5 and 3x - 5 ≥ 7.

a.
Graph C
b.
Graph A
c.
Graph B
d.
Graph D


Solution:

2 + x > 5 and 3x - 5 ≥ 7
x > 3 and 3x ≥ 12
x > 3 and x ≥ 4

The intersection of the solution sets is the same as the solution set of the sentence x ≥ 4.

So, Graph C is the correct choice.


Correct answer : (1)
 3.  
Choose the graph which is the solution set of the disjunction 4z - 3 ≥ 41 or 3z + 5 ≤ 23.


a.
Graph B
b.
Graph A
c.
Graph C
d.
Graph D


Solution:

4z - 3 ≥ 41 or 3z + 5 ≤ 23

4z ≥ 44 or 3z ≤ 18

z ≥ 11 or z ≤ 6

The union of the solution sets is similar to that in graph A.


Correct answer : (2)
 4.  
Find the solution set of the disjunction x + 2 < - 10 or x - 2 > 9.
a.
{ x: - 12 < x < 11 }
b.
{ x: x > 11 or x < 9 }
c.
{ x: x > - 11 or x < - 12 }
d.
{ x: x < - 12 or x > 11 }


Solution:

x + 2 < - 10 or x - 2 > 9

x < - 12 or x > 11

The solution set is: {x: x < - 12 or x > 11}.


Correct answer : (4)
 5.  
Find the solution set of the disjunction x + 3 > 6 or 2x - 2 ≤ - 12.
a.
{x: x > 9 or x ≤ 12}
b.
{x: x > 3 or x ≤ - 12}
c.
{ x: x ≤ - 5 or x > 3}
d.
{x: x > 6 or x ≤ - 6}


Solution:

x + 3 > 6 or 2x - 2 ≤ - 12

x > 3 or 2x ≤ - 10

x > 3 or x ≤ - 5
[Simplify.]

The solution set is: {x: x ≤ - 5 or x > 3}


Correct answer : (3)
 6.  
Solve the conjunction 3(x + 7) ≥ 6 and 2(2 + x)7 ≥ 2.
a.
{x: x ≥ 2 and x ≤ 2}
b.
{x: x ≥ 5}
c.
{x: 2 < x < 6}
d.
{x: x > 7 and x < 2}


Solution:

3(x + 7) ≥ 6 and 2(2 + x)7 ≥ 2

x + 7 ≥ 2 and 2(2 + x) ≥ 14

x ≥ - 5 and 2 + x ≥ 7

x ≥ - 5 and x ≥ 5

Therefore, the solution set of conjunction is {x: x ≥ 5}.


Correct answer : (2)
 7.  
Find the solution set of the disjunction 6 + 11m < 5m - 30 or 2(4 + 5m) + 6 > 64.
a.
{m: m < - 6 or m > 5}
b.
{m: m > 5 or m < 4}
c.
{m: m < 30 or m > 64}
d.
{m: m ≤ 10 or m > 6}


Solution:

6 + 11m < 5m - 30 or 2(4 + 5m) + 6 > 64

11m < 5m - 36 or 2(4 + 5m) > 58
[Simplify.]

6m < - 36 or 8 + 10m > 58

m < - 6 or 10m > 50

m < - 6 or m > 5

The solution set is: {m: m < - 6 or m > 5}


Correct answer : (1)
 8.  
Find the solution set of the disjunction. 2(4x + 4) ≥ 58 or 2(2x-3)3 ≤ 6 .
a.
{x: x ≥ 58 or x ≤ 6}
b.
{x: x > 4 or x < 3}
c.
{x: x ≥ 7 or x ≤ 6 }
d.
{x: x < 2 and x > - 1}


Solution:

2(4x + 1) ≥ 58 or 2(2x-3)3 ≤ 6

8x + 2 ≥ 58 or 2(2x - 3) ≤ 18

8x ≥ 56 or 4x - 6 ≤ 18

x ≥ 7 or 4x ≤ 24

x ≥ 7 or x ≤ 6

The solution set is: {x: x ≥ 7 or x ≤ 6 }


Correct answer : (3)
 9.  
Find the solution set of 5(2s + 2) - 42s > 39 and 29(s - 2) < 41(s - 2).
a.
{s: s > 39 and s < 41}
b.
{s: s > 29 or s < 2}
c.
{s: 2 < s < 29}
d.
f


Solution:

5(2s + 2) - 9s > 39 and 42(s - 2) < 41(s - 2)

10s + 10 - 9s > 39 and 42s - 84 < 41s - 82

s + 10 > 39 and 42s < 41s + 2

s > 29 and s < 2

There is no value for s which simultaneously satisfies both the inequalities.

The Solution set = { } = f


Correct answer : (4)
 10.  
Find the solution set of 6(t - 3) - 5(t - 3) > 4 and 4(2t - 1) - 2(2t - 3) < 14
a.
f
b.
{t: t > 4 or t < 14}
c.
{t: 3 < t < 7}
d.
{t: 4 < t < 14}


Solution:

6(t - 3) - 5(t - 3) > 4 and 4(2t - 1) - 2(2t - 3) < 14

6t - 18 - 5t + 15 > 4 and 8t - 4 - 4t + 6 < 14

t - 3 > 4 and 4t + 2 < 14

t > 7 and 4t < 12

t > 7 and t < 3

There are no values for t that are both greater than 7 and less than 3.

The solution set = { } = f


Correct answer : (1)

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