Chapter 1

The expression \(8 x^{2}\) means A. \(8 \cdot x \cdot 2\) B. \(8 \cdot x \cdot x\) C. \(8+x^{2}\) D. \(8 x \cdot 8 x\)

Fill in each blank with one of the following. positive,negative,0 The product or the quotient of two numbers with the same sign is ______

Decide whether each statement is true \(o r\) false. If it is false, explain why. $$ 3^{2}=6 $$

Complete each of the following. The sum of a number and its opposite will always be

Which is an example of a term with numerical coefficient \(5 ?\) A. \(5 x^{3} y^{7}\) B. \(x^{5}\) C. \(\frac{x}{5}\) D. \(-5 x y^{3}\)

The natural numbers, their additive inverses, and 0 form the set of _________.

If \(x=2\) and \(y=1,\) then the value of \(x y\) is A. \(\frac{1}{2}\) B. 1 C. 2 D. 3

Fill in each blank with one of the following. positive,negative,0 The product or the quotient of two numbers with different signs is _____

Complete each of the following. When adding a positive number and a negative number, where the negative number has the greater absolute value, the sum will be a (positive/negative) number. Give a number-line illustration using the sum \(-4+2\).

Which is an example of a pair of like terms? A. \(6 t, 6 w\) B. \(-8 x^{2} y, 9 x y^{2}\) C. \(5 r y, 6 y r\) D. \(-5 x^{2}, 2 x^{3}\)

The additive inverse of every negative number is a (negative / positive) number.

The sum of 15 and a number \(x\) is represented by A. \(15+x\) B. \(15-x\) C. \(x-15\) D. \(15 x\)

Fill in each blank with one of the following. positive,negative,0 If three negative numbers are multiplied, the product is _______

Which is a correct translation for "six times a number, subtracted from the product of eleven and the number" (if \(x\) represents the number)? A. \(6 x-11 x\) B. \(11 x-6 x\) C. \((11+x)-6 x\) D. \(6 x-(11+x)\)

If \(x\) and \(y\) are real numbers with \(x>y,\) then \(x\) lies to the (left / right) of \(y\) on a number line.

7 less than a number \(x\) is represented by A. \(7-x\) B. \(7

Fill in each blank with one of the following. positive,negative,0 If two negative numbers are multiplied and then their product is divided by a negative number, the result is ________

A student simplified the expression \(7 x-2(3-2 x)\) incorrectly as shown. $$\begin{aligned}7 x &-2(3-2 x) \\\&=7 x-2(3)-2(2 x) \\\&=7 x-6-4 x \\\&=3 x-6\end{aligned}$$

Which of the following is a solution of the equation \(3 x-1=5 ?\) A. 0 B. 2 C. 4 D. 6

Decide whether each statement is true \(o r\) false. If it is false, explain why. When evaluated, \(4+3(8-2)\) is equal to 42 .

Complete each of the following. "The difference of 7 and 12 " translates as ____________ while "the difference of 12 and \(7 "\) translates as ______________

A student simplified the expression \(3+2(4 x-5)\) incorrectly as shown. $$\begin{aligned}3+& 2(4 x-5) \\\&=5(4 x-5) \\\&=5(4 x)+5(-5) \\\&=20 x-25\end{aligned}$$

Which of the following are expressions? A. \(6 x=7\) B. \(6 x+7\) C. \(6 x-7\) D. \(6 x-7=0\)

Fill in each blank with one of the following. positive,negative,0 The reciprocal of a negative number is _______

Suppose that \(x\) represents a positive number and \(y\) represents a negative \mathrm{number. Determine whether the given expression represents a positive or } a \text { negative number. } $$ x-y $$

Simplify each expression. \(4 r+19-8\)

The additive inverse of -5 is _________, while the additive inverse of the absolute value of -5 is _________.

The value of \(5 x^{2}\) for \(x=4\) was found incorrectly as follows. $$ \begin{array}{l} 5 x^{2} \\ =5 \cdot 4^{2} \\ =20^{2} \\ =400 \end{array} $$ Find the correct value of the expression.

For each expression, label the order in which the operations should be performed. Do not actually perform them. $$ 18-2+3 $$

Fill in each blank with one of the following. positive,negative,0 If three positive numbers, five negative numbers, and zero are multiplied, the product is ______

Suppose that \(x\) represents a positive number and \(y\) represents a negative \mathrm{number. Determine whether the given expression represents a positive or } a \text { negative number. } $$ y-x $$

Simplify each expression. \(7 t+18-4\)

The value of \(\frac{x+3}{5}\) for \(x=10\) was found incorrectly as follows. $$ \begin{array}{l} \frac{x+3}{5} \\ =\frac{10+3}{5} \\ =2+3 \\ =5 \end{array} $$ Find the correct value of the expression.

Fill in each blank with one of the following. positive,negative,0 The cube of a negative number is ______

For each expression, label the order in which the operations should be performed. Do not actually perform them. $$ 28-6 \div 2 $$

Suppose that \(x\) represents a positive number and \(y\) represents a negative \mathrm{number. Determine whether the given expression represents a positive or } a \text { negative number. } $$ y-|x| $$

Simplify each expression. \(7 t+18-4\)

Match each expression in Column I with its value in Column II. Choices in Column II may be used once, more than once, or not at all. I (a) |-9| (b) \(-(-9)\) (c) \(-|-9|\) (d) \(-|-(-9)|\) II A. 9 B. -9 C. Neither A nor B D. Both A and B

Evaluate each expression for (a) \(x=4\) and \((b) x=6\). \(x+7\)

Complete this statement: The quotient formed by any nonzero number divided by 0 is ______ and the quotient formed by 0 divided by any nonzero number is ______ Give an example of each quotient.

For each expression, label the order in which the operations should be performed. Do not actually perform them. $$ 2 \cdot 8-6 \div 3 $$

Suppose that \(x\) represents a positive number and \(y\) represents a negative \mathrm{number. Determine whether the given expression represents a positive or } a \text { negative number. } $$ x+|y| $$

Simplify each expression. \(8(2 p-9 q)\)

Evaluate each expression for ( \(\boldsymbol{a}\) ) \(x=4\) and \((\boldsymbol{b}) x=6\). \(x-3\)

Students often say "Absolute value is always positive." Is this true? Explain.

Which expression is undefined? A. \(\frac{4+4}{4+4}\) B. \(\frac{4-4}{4+4}\) C. \(\frac{4-4}{4-4}\) D. \(\frac{4-4}{4}\)

For each expression, label the order in which the operations should be performed. Do not actually perform them. $$ 40+6(3-1) $$

Write a numerical expression for each phrase, and simplify the expression. The sum of 9 and \(-4,\) decreased by 7

Find each sum. \(-6+(-2)\)

Evaluate the following expressions. $$25-(6-2) \text { and }(25-6)-2$$ Does it appear that subtraction is associative?