# Simplifying Variable Expressions Worksheet

Simplifying Variable Expressions Worksheet
• Page 1
1.
Jason gets $14 a day by washing cars. He is paid an extra$4 for every car he washes after 6 p.m. Which of the following equations represents his total earnings for the day, if $y$ represents his earnings per day and $x$ represents the number of cars washed after 6 p.m.?
 a. $y$ = 14 + 4$x$ b. $y$ = 4 + 14$x$ c. $y$ = 4 + 15$x$ d. None of the above

#### Solution:

Total earnings = Daily wage + Earnings for washing cars after 6 P.M. = $14 +$(4 x number of cars)

So, the equation y = 14 + 4x represents his total earnings for the day.

2.
Which of the following expressions is the simplest form of 7$m$ + 4(4 + $h$)?
 a. 7$m$ + 4$h$ + 16 b. 7$m$ + 16$h$ + 16 c. $m$ + 16$h$ + 4 d. None of the above

#### Solution:

7m + 4(4 + h) = 7m + 4(4) + 4(h)

= 7m + 16 + 4h
[Multiply.]

= 7m + 4h + 16

3.
Which of the following expressions has two terms?
 a. 7$x$ b. $\mathrm{xy}$ c. $x$ + $y$ + $\mathrm{xy}$ d. 6 + 7

#### Solution:

A term is a number or a variable or a product of numbers and variables.

x, y and xy are the three terms in the expression x + y + xy.

xy is the only term in the expression xy.

7x is the only term in the expression 7x.

6 and 7 are the two terms in the expression 6 + 7.

So, 6 + 7 is the expression, which has two terms.

4.
Which of the following expressions is equivalent to the expression 2 + 4(3 + $s$)?
 a. 15 + 4$s$ b. 13 + 4$s$ c. 14 + 4$s$ d. 16 + 4$s$

#### Solution:

2 + 4(3 + s)
[Original expression.]

= 2 + 4(3) + 4(s)
[Use the distributive property of addition.]

= 2 + 12 + 4s
[Multiply.]

= 14 + 4s
[Combine like terms.]

5.
Which of the following expressions is the simplified form of 4$x$ + 5$x$(3 + $y$)?
 a. 19$x$ + 5$x$$y$ b. 24$x$$y$ c. 19$x$ + 5($x$ + $y$) d. 19$x$ + 15 + 5$y$

#### Solution:

4x + 5x(3 + y)
[Original expression.]

= 4x + 5x(3) + 5x(y)
[Use the distributive property of addition.]

= 4x + 15x + 5xy
[Multiply.]

= (4 + 15)x + 5xy
[Use the distributive property of addition.]

= 19x + 5xy
[Simplify inside the grouping symbols.]

6.
Which of the following expressions is equivalent to the expression 5$h$ - 2$h$($x$ - $m$)?
 a. 5$h$ - 2$h$$x$ b. 5$h$ - 2$h$$x$ + 2$h$$m$ c. 5$x$$h$$m$ d. $h$($x$ - $m$)

#### Solution:

5h - 2h(x - m)
[Original expression.]

= 5h - 2h(x) - 2h(- m)
[Use the distributive property of addition.]

= 5h - 2hx + 2hm
[Multiply.]

7.
Fill in the blanks.
7$h$ + 3 - 4$h$ - 3 - 9$h$ + 3 = __ $h$ + __
 a. -6, -3 b. 6, 3 c. 6, -3 d. -6, 3

#### Solution:

L.H.S = 7h + 3 - 4h - 3 - 9h + 3

= 7h - 4h - 9h + 3 - 3 + 3
[Use the commutative property of addition.]

= (7 - 4 - 9)h + (3 - 3 + 3)
[Use the distributive property of addition.]

= -6h + 3
[Combine like terms.]

The coefficient of h is -6 and the constant is 3.

-6, 3 is the set of values that fill in the blanks in the equation.

8.
Which of the following is the simplest form of the expression given below?
($a$ + 3 - 4$a$ - 3 + 5$a$ - 2 + 3$a$)
 a. 5$a$ - 2 b. 5$a$ + 2 c. - 5$a$ - 2 d. - 5$a$ + 2

#### Solution:

(a + 3 - 4a - 3 + 5a - 2 + 3a)
[Original expression.]

= (a - 4a + 5a + 3a) + (3 - 3 - 2)
[Use the commutative property of addition to reorder the terms.]

= 5a - 2
[Combine like terms.]

Among the choices, the expression 5a - 2 is the simplified form of the expression.

9.
Which expression has two variables?
 a. $x$ + $y$ + $x$$y$ b. 4 + $x$ c. 5$x$ d. 4 + 5

#### Solution:

Variable is a symbol, usually a letter, which stands for an unknown number.

Choice (A) consists of variables x and y.

Choice (B) consists of one variable x and one constant 4.

Choice (C) consists of one variable x.

Choice (D) consists of two constants 4 and 5.

Only choice A contains two variables.

10.
Which of the following gives the total money (expressed in dollars) spent by Nina, if she bought four toys for $d$ dimes each, two cups for $n$ nickels each and a basket for $1.63?  a.$($d$ + $n$ + 1.63) b. $($d$ + $n$ - 1.63) c.$(4$d$ + 0.1$n$ + 1.63) d. $(0.4$d$ + 0.1$n$ + 1.63) #### Solution: Cost of 4 toys = 4 x d dimes = 4d dimes 10 dimes = 1 dollar [Write dimes in terms of dollars.] 1 dime = 110 dollar [Divide each side by 10.] Cost of 4 toys = 4d x 110 =$0.4d

Cost of 2 cups = 2 x n nickels = 2n nickels

20 nickels = 1 dollar
[Write nickels in terms of dollars.]

1 nickel = 120 dollar
[Divide each side by 20.]

Cost of 2 cups = 2n x 120 = $0.1n Total amount =$(0.4d + 0.1n + 1.63)