﻿ Solving Compound Sentences with Inequalities Worksheet | Problems & Solutions

# Solving Compound Sentences with Inequalities Worksheet

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

2.
Choose the graph which is the solution set of the conjunction 2 + $x$ >5 and 3$x$ - 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.

3.
Choose the graph which is the solution set of the disjunction 4$z$ - 3 ≥ 41 or 3$z$ + 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.

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}.

5.
Find the solution set of the disjunction $x$ + 3 > 6 or 2$x$ - 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}

6.
Solve the conjunction 3($x$ + 7) ≥ 6 and ≥ 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}.

7.
Find the solution set of the disjunction 6 + 11$m$ < 5$m$ - 30 or 2(4 + 5$m$) + 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}

8.
Find the solution set of the disjunction. 2(4$x$ + 4) ≥ 58 or $\frac{2\left(2x-3\right)}{3}$ ≤ 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 }

9.
Find the solution set of 5(2$s$ + 2) - 42$s$ > 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

10.
Find the solution set of 6($t$ - 3) - 5($t$ - 3) > 4 and 4(2$t$ - 1) - 2(2$t$ - 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