Chapter 2

In Exercises \(55-58\), write an algebraic equation. Do not solve the equation. A high school earned \(\$ 986\) in revenue for a play. Tickets for the play cost \(\$ 10\) for adults and \(\$ 6\) for students. The number of students attending the play was \(\frac{3}{4}\) the number of adults attending the play. How many adults and student attended the play?

When constructing a verbal model from a written statement, what are some key words and phrases that indicate the four operations of arithmetic?

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ 3-2[6+(4-x)] $$

In Exercises 57-60, write an algebraic expression for the statement. $$ \text { The income earned at } \$ 7.55 \text { per hour for } w \text { hours } $$

In Exercises \(55-58\), write an algebraic equation. Do not solve the equation. An ice show earns a revenue of \(\$ 11,041\) one night. Tickets for the ice show cost \(\$ 18\) for adults and \(\$ 13\) for children. The number of adults attending the ice show was 33 more than the number of children attending the show. How many adults and children attended the show?

What is a hidden operation in a verbal phrase? Explain how to identify hidden operations.

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ 10 x+5[6-(2 x+3)] $$

In Exercises 57-60, write an algebraic expression for the statement. The cost for a family of \(n\) people to see a movie when the cost per person is \(\$ 8.25\)

Are there any equations of the form \(a x=b(a \neq 0)\) that are true for more than one value of \(x\) ? Explain.

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ 7 x(2-x)-4 x $$

In Exercises 57-60, write an algebraic expression for the statement. $$ \text { The cost of } m \text { pounds of meat when the cost per pound is } \$ 3.79 $$

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ -6 x(x-1)+x^{2} $$

In Exercises 57-60, write an algebraic expression for the statement. The total weight of \(x\) bags of fertilizer when each bag weighs 50 pounds

Determine which equations are equivalent to \(14=x+8\). (a) \(x+8=14\) (b) \(8 x=14\) (c) \(x-8=14\) (d) \(8+x=14\) (e) \(2(x+4)-x=14\) (f) \(3(x+6)-2 x+5=14\)

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ 4 x^{2}+x(5-x)-3 $$

Explain the difference between simplifying an expression and solving an equation. Give an example of each.

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ -z(z-2)+3 z^{2}+5 $$

In Exercises \(63-68\), simplify the expression. $$ t^{2} \cdot t^{5} $$

In Exercises 63-68, translate the verbal phrase into an algebraic expression. Simplify the expression. $$ x \text { times the sum of } x \text { and } 3 $$

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ -3 t(4-t)+t(t+1) $$

In Exercises \(63-68\), simplify the expression. $$ \left(-3 y^{3}\right) y^{2} $$

In Exercises 63-68, translate the verbal phrase into an algebraic expression. Simplify the expression. $$ n \text { times the difference of } 6 \text { and } n $$

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ -2 x(x-1)+x(3 x-2) $$

In Exercises \(63-68\), simplify the expression. $$ 6 x+9 x $$

In Exercises 63-68, translate the verbal phrase into an algebraic expression. Simplify the expression. $$ x \text { minus the sum of } 25 \text { and } x $$

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ 3 t[4-(t-3)]+t(t+5) $$

Are the expressions \(-3^{2}\) and \((-3)^{2}\) equivalent? Explain.

In Exercises \(63-68\), simplify the expression. $$ 4-3 t+t $$

In Exercises 63-68, translate the verbal phrase into an algebraic expression. Simplify the expression. $$ \text { The sum of } 4 \text { and } x \text { added to the sum of } x \text { and }-8 $$

In Exercises \(47-66\), simplify the expression by removing symbols of grouping and combining like terms. $$ 4 y[5-(y+1)]+3 y(y+1) $$

Do you always have to use \(x\) to represent an unknown value when writing an algebraic expression? Give an example of when you may want to use another letter.

In Exercises \(63-68\), simplify the expression. $$ -(-8 b) $$

In Exercises 63-68, translate the verbal phrase into an algebraic expression. Simplify the expression. $$ \text { The square of } x \text { decreased by the product of } x \text { and } 2 x $$

In Exercises 67 and 68, write and simplify expressions for (a) the perimeter and (b) the area of the rectangular sandboxes. \(4 x \mathrm{ft}\) $$ (x+5) \mathrm{ft} $$

Name four mathematical operations you can use to write an algebraic expression.

In Exercises \(63-68\), simplify the expression. $$ 7(-10 x) $$

In Exercises 63-68, translate the verbal phrase into an algebraic expression. Simplify the expression. $$ \text { The square of } x \text { added to the product of } x \text { and } x+1 $$

What value of \(y\) would cause \(3 y+2\) to equal 8 ? Explain.

In Exercises 69-72, translate the phrase into an algebraic expression. Let \(x\) represent the real number. $$ 23 \text { more than } x $$

Pens cost \(\$ 0.25\) each. Pencils cost \(\$ 0.10\) each. Write an algebraic expression that represents the total cost of buying \(p\) pens and \(n\) pencils.

In Exercises 69-72, translate the phrase into an algebraic expression. Let \(x\) represent the real number. $$ c \text { divided by } 6 $$

A consumer buys \(g\) gallons of gasoline for a total of \(d\) dollars. Write an algebraic expression that represents the price per gallon.

In Exercises 69 and 70, identify the variable(s) in the expression. $$ 3^{2}+z $$

Describe the pattern and use your description to find the value of the expression when \(n=20\). $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \boldsymbol{n} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \begin{array}{l} \text { Value of } \\ \text { expression } \end{array} & -1 & 1 & 3 & 5 & 7 & 9 \\ \hline \end{array} $$

Like Terms In your own words, state the definition of like terms. Give an example of like terms and an example of unlike terms.

In Exercises 69 and 70, identify the variable(s) in the expression. $$ 3(x+5)+10 $$

In Exercises 69-72, translate the phrase into an algebraic expression. Let \(x\) represent the real number. $$ \text { Nine times the difference of } h \text { and } 3 $$

Find values for \(a\) and \(b\) such that the expression \(a n+b\) yields the values in the table. $$ \begin{array}{|l|c|c|c|c|c|c|} \hline \boldsymbol{n} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \boldsymbol{a n}+\boldsymbol{b} & 4 & 9 & 14 & 19 & 24 & 29 \\ \hline \end{array} $$

Describe how to combine like terms. Give an example of an expression that can be simplified by combining like terms.

In Exercises 69 and 70, identify the variable(s) in the expression. $$ \frac{6}{t}-22 $$