Chapter 1

Describe the order of operations agreed upon by mathematicians.

Consider the verbal phrase: the difference of 7 and a number \(\boldsymbol{n}\). What operation does the word difference indicate?

In the expression \(15^{3},\) what is 15 called? What is 3 called? What is the expression called?

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$3 x+1=14$$

Explain what \(data\) are and give an example.

A function is a relationship between two quantities, called the ___ and the ____.

Explain what it means to evaluate \(a\) variable expression.

If an expression without grouping symbols includes addition and an exponent, which operation should you do first?

Consider the verbal phrase: the difference of 7 and a number \(\boldsymbol{n}\). Translate the verbal phrase into an algebraic expression.

The expressions \(3 x^{2}\) and \((3 x)^{2}\) do not have the same meaning. Explain the difference.

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$7 y-6$$

What kind of graph is useful for showing changes over time?

The collection of all input values is the ____ of the function. The collection of all output values is the ___ of the function.

What operation is indicated by the expression? a. \(4 y\) b. \(\frac{7}{d}\) c. \(t+8\) d. \(3-t\)

If an expression without grouping symbols includes multiplication and division, which operation should you do first?

Evaluate the expressions \(3 x^{2}\) and \((3 x)^{2}\) when \(x=4\)

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$\left(y^{2}+4\right)-7$$

Four ways to represent a function are (1) ____ , (2) ___ , (3) ___ , and (4) ____ .

Write a variable expression for "5 divided by \(r\)."

Evaluate the expression for the given value of the variable. $$x^{4}-3 \text { when } x=2$$

Describe how to use a verbal model to solve a problem.

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$5 x-1=3+x$$

For a relationship to be a function, it must be true that for each input, there is exactly one output. Does the table represent a function? Explain. $$ \begin{array}{|c|c|} \hline \text { Input } & \text { Output } \\ \hline 1 & 3 \\ \hline 2 & 4 \\ \hline 3 & 5 \\ \hline 4 & 6 \\ \hline \end{array} $$

How is unit analysis helpful in solving real-life problems?

Evaluate the expression for the given value of the variable. $$5 \cdot 6 y \text { when } y=5$$

Match the verbal phrase with its corresponding algebraic expression. A. \(4 x-11\) B. \(4(x-11)\) c. \(11-4 x\) D. \(11 x+4\) Eleven decreased by the quantity four times a number \(x\)

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$3 x+2 \leq 8$$

For a relationship to be a function, it must be true that for each input, there is exactly one output. Does the table represent a function? Explain. $$ \begin{array}{|c|c|} \hline \text { Input } & \text { 0utput } \\ \hline 1 & 3 \\ \hline 2 & 3 \\ \hline 3 & 4 \\ \hline 4 & 4 \\ \hline \end{array} $$

Evaluate the expression when \(y=6\). \(5 y\)

$$a^{3}+10 a \text { when } a=3$$

Match the power with the words that describe it. A. five to the sixth power B. two to the fifth power C. five squared D. five cubed $$ 2^{5} $$

Decide whether the following is an expression, an equation, or an inequality. Explain your decision. $$5 x>20$$

Evaluate the expression when \(y=6\). $$ \frac{24}{y} $$

Evaluate the expression for the given value of the variable. $$\frac{16}{x}-2 \text { when } x=4$$

Match the verbal phrase with its corresponding algebraic expression. A. \(4 x-11\) B. \(4(x-11)\) c. \(11-4 x\) D. \(11 x+4\) Four times the quantity of a number \(x\) minus eleven

Identify the left side and the right side of the equation \(8+3 x=5 x-9\)

Evaluate the expression for the given value of the variable. $$\frac{22}{x} \div 2+16 \text { when } x=11$$

Match the verbal phrase with its corresponding algebraic expression. A. \(4 x-11\) B. \(4(x-11)\) c. \(11-4 x\) D. \(11 x+4\) Four times a number \(x\) decreased by eleven

Evaluate the expression when \(x=3\) $$ x^{2} $$

Jan says her work shows that 6 is not a solution of \(3 x-4=14 .\) What is a likely explanation for her error?

Evaluate the expression for the given value of the variable. $$\frac{16}{n}+2^{3}-10 \text { when } n=8$$

Write the verbal sentence as an equation or an inequality. A number \(x\) increased by ten is 24

Evaluate the expression when \(x=3\) $$ (x+1)^{3} $$

$$ y \div 3 $$

Evaluate the expression for the given value of the variable. $$(x+5) \div 4 \text { when } x=9$$

Write the verbal sentence as an equation or an inequality. The product of seven and a number \(y\) is 42

ELECTIONS The number of votes received by the new student council president is represented by \(x\). Match the sentence with the equation or inequality that represents it. A. \(x=125\) B. \(x<125\) c. \(x \geq 125\) D. \(x \leq 125\) She received no more than 125 votes.

Evaluate the expression when \(x=3\) $$ 2 x^{2} $$

Does the table represent a function? Explain. $$ \begin{array}{|c|c|} \hline \text { Input } & \text { Output } \\ \hline 5 & 3 \\ \hline 6 & 4 \\ \hline 7 & 5 \\ \hline 8 & 6 \\ \hline \end{array} $$

Evaluate the expression for the given value of the variable. $$b+6 \div 4 \text { when } b=1.5$$