﻿ Evaluating Variable Expressions Worksheets | Problems & Solutions Evaluating Variable Expressions Worksheets

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

= 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

2.
Simplify.
| 3$a$ - 9$b$ | + | 2$b$ + 6$a$ | - 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

= 57.6
[Subtract 8.4 from 66.]

3.
Evaluate | 8$x$ - 2$y$ | + | 5$y$ - 2$x$ | 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 |

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

= 91
[Simplify.]

4.
Evaluate $\frac{8}{2}$ + | 15 - 3$x$ | + 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.]

5.
Evaluate 7.5 + | 2$a$ - 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 |

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

= 18.5
[Simplify.]

6.
The cost of $n$ pens is given by the expression $24$n$. 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.]

7.
Find the value of the expression - $\frac{171}{x}$, 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.]

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.]

9.
Which of these would you get by evaluating the expression 24 - 4$y$, 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.]

10.
Evaluate the expression 49$y$, 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.