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Inequality Worksheets

Inequality Worksheets
  • Page 1
 1.  
Are the two inequalities equivalent? - 7x < 35 and - x < 5
a.
Yes
b.
No


Solution:

- 7x < 35
[First inequality.]

- x < 5
[Divide throughout by 7.]

- x < 5
[Second inequality.]

If two inequalities have the same solution set, then they are called equivalent inequalities.

So, the two inequalities are equal.


Correct answer : (1)
 2.  
Are the two inequalities equivalent? 3x - 5 ≤ 13 and 3x ≥ 18
a.
Yes
b.
No


Solution:

3x - 5 ≤ 13
[First inequality.]

3x ≤ 18
[Add 5 to both sides of the equation.]

3x ≥ 18
[Second inequality.]

If the two inequalities have the same solution set, then they are called equivalent inequalities.

So, the given inequalities are not equal.


Correct answer : (2)
 3.  
Solution for the inequality is given in set-builder notation. Solve and choose the correct one for the inequality given.
7 [2x - (x + 7)] < 3 (2x - 3)
a.
{x: x < - 40}
b.
{x: x < 58}
c.
{x: x < 40}
d.
{x: x < - 58}


Solution:

7 [2x - (x + 7)] < 3(2x - 3)

14x - 7(x + 7) < 3(2x - 3)
[Distributive property.]

14x - 7x - 49 < 6x - 9
[Distributive property.]

7x - 49 < 6x - 9
[Group the like terms.]

x - 49 < - 9
[Subtracting 6x from the two sides of the equation.]

x < 40
[Add 49 to both sides of the equation.]

The solution set is {x: x < 40}


Correct answer : (3)
 4.  
Solution for the inequality is given in set-builder notation. Solve and choose the correct one for the inequality given.
3[2y + (3y - 1)] ≥ 5(2y + 1)
a.
{y: y ≤ 1.6}
b.
{y: y ≥ 2.6}
c.
{y: y ≥ 1.6}
d.
{y: y ≤ - 1.6}


Solution:

3 [2y + (3y - 1)] ≥ 5 (2y + 1)

6y + 3 (3y - 1) ≥ 5 (2y + 1)
[Distributive property.]

6y + 9y - 3 ≥ 10y + 5
[Distributive property.]

15y - 3 ≥ 10y + 5
[Add like terms.]

5y - 3 ≥ 5
[Subtracting 10y from the two sides of the equation.]

5y ≥ 8
[Add 3 to both sides of the equation.]

y8 / 5
[Divide throughout by 5 .]

y ≥ 1.6

The solution set is {y: y ≥ 1.6}


Correct answer : (3)
 5.  
The difference of the measures of any two sides of a triangle is always less than the measure of the third side. In a triangle ABC, BC = 6 and AC = 4 + AB. Then measure of AB will be:
a.
Less than 1
b.
Greater than 1
c.
Equal to 1


Solution:

The difference of the measures of any two sides of a triangle is always less than the measure of the third side.

So, BC - AC < AB

6 - (4 + AB) < AB
[Substitute the values.]

2 - AB < AB

2 < 2AB
[Add AB to both sides of the equation.]

1 < AB
[Divide throughout by 2.]

So, AB > 1


Correct answer : (2)
 6.  
Katie can spend at most $788.10 on a television, which includes 6.5% sales tax. Find the maximum price of the television which she can buy.
a.
$788.10
b.
$106.50
c.
$704
d.
$740


Solution:

Let x be the maximum price of the television.

So, sales tax = 6.5x100
[Sales Tax = 6.5%.]

She can afford a maximum of $788.10.

x + 6.5x100 ≤ 788.10
[Amount she has to spend = Price of the television + sales tax.]

100x + 6.5x100 ≤ 788.10

106.5x100 ≤ 788.10
[Simplify.]

x788.10 ×100106.5

x ≤ $740

So, the maximum price of the television Katie can afford to buy is $740.


Correct answer : (4)
 7.  
Solve for x.
5ax + 8b < 2ax - 6b, a < 0
a.
{x: x > - 14b3a }
b.
{x: x < - 14b3a }
c.
{x: x < 14b3a }
d.
{x: x > 14b3a }


Solution:

5ax + 8b < 2ax - 6b, a < 0

3ax + 8b < - 6b
[Subtracting 2ax from the two sides of the equation.]

3ax < -14b
[Subtracting 8b from the two sides of the equation.]

Given a < 0, hence it is a negative value. The inequality sign will change when dividing by 3a.

x > - 14b3a

So, the solution set is {x: x > - 14b3a }


Correct answer : (1)
 8.  
Determine whether a - b > 0 when a > b.
a.
No
b.
Yes


Solution:

a - b > 0 when a > b is true. Because, the addition or subtraction of any real number does not affect the inequality.

a > b

a - b > 0
[Subtracting b from the two sides of the inequality.]


Correct answer : (2)
 9.  
Tim has $25. He wants to buy some pens and each pen costs 73 cents. Find the maximum number of pens that Tim can buy.
a.
35
b.
32
c.
33
d.
34


Solution:

Let x be the number of pens Tim can buy.

Total cost of x pens = $73 / 100 x
[73 cents = $73 / 100.]

The amount with Tim is only $25. So, the total price of the pens shall not exceed $25.

73 / 100 x ≤ 25
[Express as a relation.]

73x ≤ 2500
[Multiply throughout by 100.]

x ≤ 34.24657

So, Tim can buy 34 pens.


Correct answer : (4)
 10.  
Gary has to take four Math tests to complete his seventh grade. On each of the tests he can score a maximum of 25. His scores on three tests are 20, 22 and 16. What should be his score in the fourth test, so that he gets a total score of at least 77 on all four tests?
a.
atmost 18
b.
atmost 19
c.
atleast 24
d.
atleast 19


Solution:

Let n be the score of Gary in his fourth test.

n + 20 + 22 + 16 ≥ 77

n + 58 ≥ 77
[Simplify.]

n + 58 - 58 ≥ 77 - 58
[Subtracting 58 from the two sides of the equation.]

n ≥ 19
[Simplify.]

Gary should get at least 19 points in his fourth test.


Correct answer : (4)

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Solving Multi-step Inequalities Worksheet Inequality Word Problems
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