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Evaluating Variable Expressions Worksheets

Evaluating Variable Expressions Worksheets
  • Page 1
 1.  
If a = 3, b = 2.5, c = - 3, evaluate 5 | 2a + 4b | - 3 | 2b - 6c | + | 3a + 2c |.
a.
14
b.
8
c.
16
d.
11


Solution:

5 | 2a + 4b | - 3 | 2b - 6c | + | 3a + 2c |
[Original expression.]

= 5 | 2(3) + 4(2.5) | - 3 | 2(2.5) - 6(- 3) | + | 3(3) + 2(- 3) |
[Substitute a = 3, b = 2.5, c = - 3.]

= 5 | 6 + 10 | - 3 | 5 + 18 | + | 9 - 6 |
[Multiply.]

= 5 | 16 | - 3 | 23 | + | 3 |
[Add.]

= 5 (16) - 3 (23) + 3
[Absolute values of 16, 23, and 3 are 16, 23, and 3 respectively.]

= 80 - 69 + 3
[Multiply.]

= 11 + 3
[Subtract 69 from 80.]

= 14
[Add 11 and 3.]


Correct answer : (1)
 2.  
Simplify.
| 3a - 9b | + | 2b + 6a | - 8.4 if a = - 5 and b = 3
a.
57.6
b.
57.6
c.
26.4
d.
74.4


Solution:

| 3a - 9b | + | 2b + 6a | - 8.4
[Original expression.]

= | 3(- 5) - 9(3) | + | 2(3) + 6(- 5) | - 8.4
[Substitute a = - 5 and b = 3.]

= | - 15 - 27 | + | 6 - 30 | - 8.4
[Multiply.]

= | - 42 | + | - 24 | - 8.4
[Simplify.]

= 42 + 24 - 8.4
[Absolute values of -42 and -24 are 42 and 24 respectively.]

= 66 - 8.4
[Add 42 and 24.]

= 57.6
[Subtract 8.4 from 66.]


Correct answer : (2)
 3.  
Evaluate | 8x - 2y | + | 5y - 2x | if x = 7.0 and y = - 3.0.
a.
46
b.
33
c.
64
d.
91


Solution:

| 8x - 2y | + | 5y - 2x |
[Original expression.]

= | 8(7.0) - 2(- 3.0) | + | 5(- 3.0) - 2(7.0) |
[Substitute x = 7.0 and y = - 3.0.]

= | 56 + 6 | + | - 15 - 14 |
[Multiply.]

= | 62 | + | - 29 |
[Add.]

= 62 + 29
[Absolute values of 62 and -29 are 62 and 29 respectively.]

= 91
[Simplify.]


Correct answer : (4)
 4.  
Evaluate 8 2 + | 15 - 3x | + 3 if x = 6.
a.
6
b.
10
c.
9
d.
4


Solution:

8 / 2 + | 15 - 3x | + 3
[Original expression.]

= 4 + | 15 - 3x | + 3
[Divide 8 by 2.]

= 4 + | 15 - 3(6) | + 3
[Substitute x = 6.]

= 4 + | 15 - 18 | + 3
[Multiply 3 and 6.]

= 4 + | - 3 | + 3
[Subtract 18 from 15.]

= 4 + 3 + 3
[Absolute value of -3 is 3.]

= 10
[Simplify.]


Correct answer : (2)
 5.  
Evaluate 7.5 + | 2a - 5 | if a = - 3.
a.
13.5
b.
- 3.5
c.
18.5
d.
- 6.5


Solution:

7.5 + | 2a - 5 |
[Original expression.]

= 7.5 + | 2(- 3) - 5 |
[ Substitute a = - 3.]

= 7.5 + | - 6 - 5 |
[Multiply 2 and -3.]

= 7.5 + | - 11 |
[Add -6 and -5.]

= 7.5 + 11
[ Absolute value of -11 is 11.]

= 18.5
[Simplify.]


Correct answer : (3)
 6.  
The cost of n pens is given by the expression $24n. Find the cost of 6 pens.
a.
$144
b.
$24
c.
$6
d.
$150


Solution:

The cost of n pens is $24n.
[Original expression.]

To find the cost of 6 pens, substitute n = 6 in the expression.

Cost of 6 pens = $24(6)

= $144
[Multiply.]


Correct answer : (1)
 7.  
Find the value of the expression - 171x, for x = 19.
a.
8
b.
- 9
c.
- 8
d.
9


Solution:

- 171x
[Given expression.]

= - 17119
[Replace x with 19.]

= - 9
[Divide numerator and denominator by 19.]


Correct answer : (2)
 8.  
A bus travels at a constant speed of 92 miles per hour. Find the distance traveled by the bus in 4 hours.
a.
368 miles
b.
1840 miles
c.
1472 miles
d.
736 miles


Solution:

The distance that the bus travels in one hour = 92 miles

Total distance traveled by the bus in x hours = 92x
[Distance traveled = speed × time.]

Distance traveled by the bus in 4 hours = 92 × 4 = 368 miles
[Substitute.]


Correct answer : (1)
 9.  
Which of these would you get by evaluating the expression 24 - 4y, for y = 3?
a.
17
b.
15
c.
12
d.
20


Solution:

24 - 4y = 24 - 4 × 3
[Substitute y = 3.]

= 24 - 12
[Multiply.]

= 12
[Subtract.]


Correct answer : (3)
 10.  
Evaluate the expression 49y, for y = 4.
a.
200
b.
194
c.
198
d.
196


Solution:

49y
[Given expression.]

= 49 × 4
[Replace y with 4.]

= 196
[Multiply.]

So, the value of the expression 49y for y = 4, is 196.


Correct answer : (4)

More Evaluating Variable Expressions Worksheets
Variable Expressions Worksheet
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