Chapter 1

Explain what the statement \(x-y=x+(-y)\) means.

a. \(9 x-2(-3 x+4)\) b. \(9 x-2(-3 x)+4\)

When solving a linear equation in one variable, the objective is to isolate the variable on one side of the equation. What does that mean?

Explain why the order of operations rule is necessary.

Use variables to state each property of real numbers. a. Commutative property of addition b. Associative property of multiplication c. Distributive property of multiplication over addition

What two numbers are a distance of 5 away from \(-2\) on the number line?

Checking Accounts. To find the total dollar amount of the checks entered in the register below, we could add the check amounts in the order in which they are written: \(\mathrm{S} 39+\$ 75+\$ 34+\$ 25+\$ 111+\$ 16 .\) Write an expression with the amounts reordered and grouped in such a way that the addition is easier. Then find the sum. What properties of real numbers did you use? (TABLE CANNOT COPY)

Use variables to state each property of real numbers. a. Additive inverse property b. Multiplicative inverse property

Place the proper symbol ( \(>\) or \(<\) ) in the blank: $$ -4.6 \quad \square\quad-4.5 $$

Use variables to state each property of real numbers. a. Additive identity property b. Multiplicative identity property

Write the set of integers.

In each case, explain what you can conclude about one or both of the numbers. a. When the two numbers are added, the result is \(0 .\) b. When the two numbers are subtracted, the result is \(0 .\) c. When the two numbers are multiplied, the result is 0 . d. When the two numbers are divided, the result is 0 .

Use variables to state each property of real numbers. a. Division of 0 b. Division by 0

Translate into mathematical symbols: ten less than twice \(x\)

What are like terms?

Find the value of \(k\) that makes 4 a solution of the following linear equation in \(x .\) $$ k+3 x-6=3 k x-k+16 $$

True or false: The real numbers is the set of all decimals.

Use each of the words commute, associate, and distribute in a sentence in which the context is nonmathematical.

Solve: \(\quad 0.75(x-5)-\frac{4}{5}=\frac{1}{6}(3 x+1)+3.2\).

True or false: Irrational numbers are nonterminating, nonrepeating decimals.

Evaluate each expression. $$\left(-\frac{3}{2}\right)\left(\frac{7}{12}\right)$$

Insert one pair of parentheses in the expression so that its value is \(0 .\) $$ 71-1-2 \cdot 5^{2}+10 $$

Evaluate each expression. $$\frac{1}{2}-\left(-\frac{4}{5}\right)$$

Evaluate: $$ \left(\begin{array}{c} \frac{12 \div 3 \cdot 4}{\left[-9^{2}-4(-1)^{9}(20)\right]^{4}}-\sqrt{6 \sqrt{\left(-\frac{3}{2}(24)\right.})} \\ \hline|-1.5| \frac{-200}{10^{2}}||^{2}+\frac{(-2)^{3}}{-4-\frac{4+2}{1+\frac{8}{2-6}}} \end{array}\right)^{5} $$

Evaluate each expression. $$-3|4-8|+(4+2 \cdot 3)^{3}$$

Evaluate each expression. $$\left(\frac{-\sqrt{4^{3}}-5^{2}}{2 \cdot 2^{2}-\left(1^{9}-4\right)}\right)^{3}$$

Simplify: $$\frac{x}{2}+\frac{x}{3}+\frac{x}{4}+\frac{x}{5}+\frac{x}{6}$$

Fill in the blank: a. \(______ \)(0.005 x+0.02 y-0.0003 z)=50 x+200 y-3 z\( b. \left(\frac{x}{54}-\frac{1}{42}\right)=7 x-9\)

What two real numbers are their own reciprocals?

Explain how the distributive property can be used to evaluate the expression \(52.713(21)+52.713(79)\) mentally.