5.1.1: Exercises

For the following exercises, translate from algebra to words.

Exercise $\PageIndex{1}$

$50-15$

Exercise $\PageIndex{2}$

(10) $(x)$

Exercise $\PageIndex{3}$

$2 a-b$

Exercise $\PageIndex{4}$

$100 \div 33$

Exercise $\PageIndex{5}$

$3 x+5$

For the following exercises, translate from words to algebra.

Exercise $\PageIndex{6}$

15 divided by 3 .

Exercise $\PageIndex{7}$

The sum of 13 and 13.

Exercise $\PageIndex{8}$

120 minus 12 .

Exercise $\PageIndex{9}$

The product of 5 and 4.

Exercise $\PageIndex{10}$

The sum of double $x$ and 5 .

For the following exercises, translate from an English phrase to an expression.

Exercise $\PageIndex{11}$

Three times $y$ minus 7 .

Exercise $\PageIndex{12}$

$a$ divided by 2 ; then add 4.

Exercise $\PageIndex{13}$

$x$ squared minus 3 .

Exercise $\PageIndex{14}$

A rental car company charges $\$ 0.15$ per mile $m$, plus a $\$ 40$ flat fee for the rental.

Exercise $\PageIndex{15}$

A parking garage in New York City charges $\$ 20$ for the first hour, then $\$ 5$ per hour $h$.

For the following exercises, use parentheses to make the statements true.

Exercise $\PageIndex{16}$

$16 \div 4 \bullet 2+5=13$

Exercise $\PageIndex{17}$

$2^2-5+3 \bullet 2=5$

Exercise $\PageIndex{18}$

$x-3 \bullet x-2=x^2-5 x+6$

Exercise $\PageIndex{19}$

$20 x \div 5-1-5 x=0$

Exercise $\PageIndex{20}$

$5 x+3 x \div 3-7 x+1 \bullet x=0$

For the following exercises, evaluate and simplify the expression.

Exercise $\PageIndex{21}$

$x^2$ when $x=9$

Exercise $\PageIndex{22}$

$2 x+5$ when $x=3$

Exercise $\PageIndex{23}$

$(3 x+1)(4 x-6)$ when $x=2$

Exercise $\PageIndex{24}$

$x^2+3 x+8$ when $x=3$

Exercise $\PageIndex{25}$

$\left(x^2+5 x-4\right)(2 x)$ when $x=4$

Exercise $\PageIndex{26}$

$4 a+5-2 a-8$ when $a=6$

Exercise $\PageIndex{27}$

$8 a^2+4 a+9-a^2-1$ when $a=5$

Exercise $\PageIndex{28}$

Yasenia is 3 years older than Xavier. How old is Yasenia when Xavier is 18 years old?

Exercise $\PageIndex{29}$

A rental car company charges $\$ 0.15$ per mile $m$, plus a $\$ 40$ flat fee for the rental. What is the cost of the car rental if one drives 100 miles?

Exercise $\PageIndex{30}$

A parking garage in New York City charges $\$ 20$ for the first hour, then $\$ 5$ per hour $h$. What is the cost of parking for 10 hours?

For the following exercises, perform the indicated operation for the expressions.

Exercise $\PageIndex{31}$

Add $(4 x-9)+(x+12)$.

Exercise $\PageIndex{32}$

Add $\left(3 x^2+2 x+1\right)+\left(x^2-2 x+2\right)$.

Exercise $\PageIndex{33}$

Subtract $(4 x-9)-(-x+2)$.

Exercise $\PageIndex{34}$

Subtract $\left(3 x^2+5 x\right)-\left(x^2-3 x+11\right)$.

Exercise $\PageIndex{35}$

Multiply $4(x+2)$.

Exercise $\PageIndex{36}$

Multiply $2\left(3 x^2-2 x+1\right)$.

Exercise $\PageIndex{37}$

Multiply $(3 x)(x-1)$.

Exercise $\PageIndex{38}$

Multiply $(2 x-1)(x+3)$.

Exercise $\PageIndex{39}$

$\left(125 x^2+35 x-5\right) \div(5)$.

Exercise $\PageIndex{40}$

$\left(9 x^2+18 x-27\right) \div(3 x)$.