Chapter 1

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$3(2 x-3)-7(3 x-1)$$

Simplify each numerical expression. Be sure to take advantage of the properties whenever they can be used to make the computations easier. $$(2)(17)(-5)-(4)(13)(-25)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(W\)_____ \(I\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-2\left(n^{2}-4\right)-4\left(2 n^{2}+1\right)$$

Simplify each of the numerical expressions. $$2^{3}-3^{3}$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(I\)_____ \(N\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-4\left(n^{2}+3\right)-\left(2 n^{2}-7\right)$$

Simplify each of the numerical expressions. $$3^{2}-2^{4}$$

Perform the following operations with real numbers. $$0 \div(-11)$$

Use the following set designations. $$ \begin{aligned} &N=\\{x \mid x \text { is a natural number }\\} \\ &Q=\\{x \mid x \text { is a rational number }\\} \\ &W=\\{x \mid x \text { is a whole number }\\} \\ &H=\\{x \mid x \text { is an irrational number }\\} \\ &I=\\{x \mid x \text { is an integer }\\} \\ &R=\\{x \mid x \text { is a real number }\\} \end{aligned} $$ Place \(\subseteq\) or \(\nsubseteq\) in each blank to make a true statement. \(I\)_____ \(W\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$3(2 x-4 y)-2(x+9 y)$$

Simplify each of the numerical expressions. $$-5^{2}-4^{2}$$

Perform the following operations with real numbers. $$-21-39$$

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-7(2 x-3 y)+9(3 x+y)$$

Simplify each of the numerical expressions. $$-7^{2}+5^{2}$$

Perform the following operations with real numbers. $$-23-38$$

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$3(2 x-1)-4(x+2)-5(3 x+4)$$

Simplify each of the numerical expressions. $$(-2)^{3}-3^{2}$$

Perform the following operations with real numbers. $$-17.3+12.5$$

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-2(x-1)-5(2 x+1)+4(2 x-7)$$

Simplify each of the numerical expressions. $$(-3)^{3}+3^{2}$$

Perform the following operations with real numbers. $$-16.3+19.6$$

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$-(3 x-1)-2(5 x-1)+4(-2 x-3)$$

Simplify each of the numerical expressions. $$3(-1)^{3}-4(3)^{2}$$

Perform the following operations with real numbers. $$21.42-7.29$$

List the elements of each set. For example, the elements of \(\\{x \mid x\) is a natural number less than 4\(\\}\) can be listed as \(\\{1,2,3\\}\). \(\\{x \mid x\) is a natural number less than 3\(\\}\)

Simplify the algebraic expressions in Problems \(15-34\) by removing parentheses and combining similar terms. $$4(-x-1)+3(-2 x-5)-2(x+1)$$

Simplify each of the numerical expressions. $$4(-2)^{3}-3(-1)^{4}$$

Perform the following operations with real numbers. $$2.73-8.14$$

List the elements of each set. For example, the elements of \(\\{x \mid x\) is a natural number less than 4\(\\}\) can be listed as \(\\{1,2,3\\}\). \(\\{x \mid x\) is a natural number greater than 3\(\\}\)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(3 x+7 y, \quad x=-1\) and \(y=-2\)

Simplify each of the numerical expressions. $$7(2)^{3}+4(-2)^{3}$$

Perform the following operations with real numbers. $$-21.4-(-14.9)$$

List the elements of each set. For example, the elements of \(\\{x \mid x\) is a natural number less than 4\(\\}\) can be listed as \(\\{1,2,3\\}\). \(\\{n \mid n\) is a whole number less than 6\(\\}\)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(5 x-9 y, \quad x=-2\) and \(y=5\)

Simplify each of the numerical expressions. $$-4(-1)^{2}-3(2)^{3}$$

Perform the following operations with real numbers. $$-32.6-(-9.8)$$

List the elements of each set. For example, the elements of \(\\{x \mid x\) is a natural number less than 4\(\\}\) can be listed as \(\\{1,2,3\\}\). \(\\{y \mid y\) is an integer greater than \(-4\\}\)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(4 x^{2}-y^{2}, x=2\) and \(y=-2\)

Simplify each of the numerical expressions. $$-3(-2)^{3}+4(-1)^{5}$$

Perform the following operations with real numbers. $$(5.4)(-7.2)$$

List the elements of each set. For example, the elements of \(\\{x \mid x\) is a natural number less than 4\(\\}\) can be listed as \(\\{1,2,3\\}\). \(\\{y \mid y\) is an integer less than 3\(\\}\)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(3 a^{2}+2 b^{2}, \quad a=2\) and \(b=5\)

Simplify each of the numerical expressions. $$5(-1)^{3}-(-3)^{3}$$

Perform the following operations with real numbers. $$(-8.5)(-3.3)$$

List the elements of each set. For example, the elements of \(\\{x \mid x\) is a natural number less than 4\(\\}\) can be listed as \(\\{1,2,3\\}\). \(\\{n \mid n\) is a positive integer greater than \(-7\\}\)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(2 a^{2}-a b+b^{2}, \quad a=-1\) and \(b=-2\)

Simplify each of the numerical expressions. $$(-3)^{2}-3(-2)(5)+4^{2}$$

Perform the following operations with real numbers. $$\frac{-1.2}{-6}$$

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(-x^{2}+2 x y+3 y^{2}, \quad x=-3\) and \(y=3\)