### Review Exercises

##### Use the Language of Algebra

**Use Variables and Algebraic Symbols**

In the following exercises, translate from algebra to English.

$12-x$

$9+2a$

$3y<15$

$32-k=7$

**Identify Expressions and Equations**

In the following exercises, determine if each is an expression or equation.

$36-6s$

$10x=120$

**Simplify Expressions with Exponents**

In the following exercises, write in exponential form.

$a\cdot a\cdot a\cdot a\cdot a$

$10\cdot 10\cdot 10$

In the following exercises, write in expanded form.

${3}^{6}$

${n}^{4}$

In the following exercises, simplify each expression.

${10}^{6}$

${4}^{3}$

**Simplify Expressions Using the Order of Operations**

In the following exercises, simplify.

$(10+2)\cdot 5$

$30+6\xf72$

${(7+5)}^{2}$

$(4+3)(10-1)$

##### Evaluate, Simplify, and Translate Expressions

**Evaluate an Expression**

In the following exercises, evaluate the following expressions.

${y}^{3}\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}y=5$

$bh\phantom{\rule{0.2em}{0ex}}\text{when}\phantom{\rule{0.2em}{0ex}}b=7,h=8$

**Identify Terms, Coefficients and Like Terms**

In the following exercises, identify the terms in each expression.

$4{x}^{3}+11x+3$

In the following exercises, identify the coefficient of each term.

$13{x}^{2}$

In the following exercises, identify the like terms.

$8,8{r}^{2},\text{8}r,3r,{r}^{2},3s$

**Simplify Expressions by Combining Like Terms**

In the following exercises, simplify the following expressions by combining like terms.

$12y+3y+y$

$6+5c+3$

$19p+5+4p-1+3p$

$13{x}^{2}-x+6+5{x}^{2}+9x$

**Translate English Phrases to Algebraic Expressions**

In the following exercises, translate the following phrases into algebraic expressions.

the sum of $10$ and twice $a$

the quotient of $s$ and $4$

$10$ less than the product of $5$ and $z$

Jack bought a sandwich and a coffee. The cost of the sandwich was $\text{\$3}$ more than the cost of the coffee. Call the cost of the coffee $c.$ Write an expression for the cost of the sandwich.

The number of poetry books on Brianna’s bookshelf is $5$ less than twice the number of novels. Call the number of novels $n.$ Write an expression for the number of poetry books.

##### Solve Equations Using the Subtraction and Addition Properties of Equality

**Determine Whether a Number is a Solution of an Equation**

In the following exercises, determine whether each number is a solution to the equation.

$d-6=21$

- ⓐ$15$
- ⓑ$27$

$20q-10=70$

- ⓐ$3$
- ⓑ$4$

$22p-6=18p+86$

- ⓐ$4$
- ⓑ$23$

**Model the Subtraction Property of Equality**

In the following exercises, write the equation modeled by the envelopes and counters and then solve the equation using the subtraction property of equality.

**Solve Equations using the Subtraction Property of Equality**

In the following exercises, solve each equation using the subtraction property of equality.

$v+8=150$

$376=n+265$

**Solve Equations using the Addition Property of Equality**

In the following exercises, solve each equation using the addition property of equality.

$k-42=113$

$501=u-399$

**Translate English Sentences to Algebraic Equations**

In the following exercises, translate each English sentence into an algebraic equation.

The difference of $15$ and $3$ is equal to $12.$

The quotient of $63$ and $9$ is equal to $7.$

The sum of five times $y$ and $4$ is $89.$

**Translate to an Equation and Solve**

In the following exercises, translate each English sentence into an algebraic equation and then solve it.

$21$ less than $a$ is $11.$

The sum of $m$ and $125$ is $240.$

**Mixed Practice**

In the following exercises, solve each equation.

$k-11=34$

$x+93=114$

$38=p+19$

$38=u-16$

##### Find Multiples and Factors

**Identify Multiples of Numbers**

In the following exercises, list all the multiples less than $50$ for each of the following.

$2$

$10$

**Use Common Divisibility Tests**

In the following exercises, using the divisibility tests, determine whether each number is divisible by $2,\text{by}\phantom{\rule{0.2em}{0ex}}3,\text{by}\phantom{\rule{0.2em}{0ex}}5,\text{by}\phantom{\rule{0.2em}{0ex}}6,\text{and by}\phantom{\rule{0.2em}{0ex}}10.$

$250$

$625$

**Find All the Factors of a Number**

In the following exercises, find all the factors of each number.

$70$

$378$

**Identify Prime and Composite Numbers**

In the following exercises, identify each number as prime or composite.

$51$

$219$

##### Prime Factorization and the Least Common Multiple

**Find the Prime Factorization of a Composite Number**

In the following exercises, find the prime factorization of each number.

$165$

$572$

**Find the Least Common Multiple of Two Numbers**

In the following exercises, find the least common multiple of each pair of numbers.

$12,20$

$18,40$

##### Everyday Math

Describe how you have used two topics from The Language of Algebra chapter in your life outside of your math class during the past month.