Chapter 1

Simplify each of the numerical expressions. $$(-2)^{2}-3(-2)(6)-(-5)^{2}$$

Perform the following operations with real numbers. $$\frac{-6.3}{0.7}$$

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 negative integer greater than \(-3\\}\)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(2 x^{2}-4 x y-3 y^{2}, \quad x=1\) and \(y=-1\)

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

Perform the following operations with real numbers. $$\left(-\frac{1}{3}\right)+\left(-\frac{3}{4}\right)$$

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 nonnegative integer less than 5\(\\}\)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(4 x^{2}+x y-y^{2}, \quad x=3\) and \(y=-2\)

Simplify each of the numerical expressions. $$-2(3)^{2}-2(-2)^{3}-6(-1)^{5}$$

Perform the following operations with real numbers. $$-\frac{5}{6}+\frac{3}{8}$$

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(3 x y-x^{2} y^{2}+2 y^{2}, \quad x=5\) and \(y=-1\)

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

Perform the following operations with real numbers. $$-\frac{3}{2}-\left(-\frac{3}{4}\right)$$

Replace each question mark to make the given statement an application of the indicated property of equality. For example, \(16=\) ? becomes \(16=16\) because of the reflexive property of equality. If \(y=x\) and \(x=-6\), then \(y=\) ? (Transitive property of equality)

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

Simplify each of the numerical expressions. $$(4-9)^{2}$$

Perform the following operations with real numbers. $$\frac{5}{8}-\frac{11}{12}$$

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(7 a-2 b-9 a+3 b, \quad a=4\) and \(b=-6\)

Simplify each of the numerical expressions. $$\left[3(-2)^{2}-2(-3)^{2}\right]^{3}$$

Perform the following operations with real numbers. $$-\frac{2}{3}-\frac{7}{9}$$

Replace each question mark to make the given statement an application of the indicated property of equality. For example, \(16=\) ? becomes \(16=16\) because of the reflexive property of equality. If \(n=2\) and \(3 n+4=10\), then \(3(?)+4=10\) (Substitution property of equality)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(-4 x+9 y-3 x-y, \quad x=-4\) and \(y=7\)

Simplify each of the numerical expressions. $$\left[-3(-1)^{3}-4(-2)^{2}\right]^{2}$$

Perform the following operations with real numbers. $$\frac{5}{6}-\left(-\frac{2}{9}\right)$$

Replace each question mark to make the given statement an application of the indicated property of equality. For example, \(16=\) ? becomes \(16=16\) because of the reflexive property of equality. If \(y=x\) and \(x=z+2\), then \(y=\) ? (Transitive property of equality)

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

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

Perform the following operations with real numbers. $$\left(-\frac{3}{4}\right)\left(\frac{4}{5}\right)$$

Replace each question mark to make the given statement an application of the indicated property of equality. For example, \(16=\) ? becomes \(16=16\) because of the reflexive property of equality. If \(4=3 x+1\), then \(?=4\) (Symmetric property of equality)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(2(a+b)^{2}, \quad a=6\) and \(b=-1\)

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

Perform the following operations with real numbers. $$\left(\frac{1}{2}\right)\left(-\frac{4}{5}\right)$$

Replace each question mark to make the given statement an application of the indicated property of equality. For example, \(16=\) ? becomes \(16=16\) because of the reflexive property of equality. If \(t=4\) and \(s+t=9\), then \(s+?=9\) (Substitution property of equality)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(-2 a-3 a+7 b-b, \quad a=-10\) and \(b=9\)

Simplify each of the numerical expressions. $$2^{4}-2(2)^{3}-3(2)^{2}+7(2)-10$$

Perform the following operations with real numbers. $$\frac{3}{4} \div\left(-\frac{1}{2}\right)$$

Replace each question mark to make the given statement an application of the indicated property of equality. For example, \(16=\) ? becomes \(16=16\) because of the reflexive property of equality. \(5 x=\) ? (Reflexive property of equality)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(3(x-2)-4(x+3), \quad x=-2\)

Simplify each of the numerical expressions. $$3(-3)^{3}+4(-3)^{2}-5(-3)+7$$

Perform the following operations with real numbers. $$\left(-\frac{5}{6}\right) \div\left(-\frac{7}{8}\right)$$

Replace each question mark to make the given statement an application of the indicated property of equality. For example, \(16=\) ? becomes \(16=16\) because of the reflexive property of equality. If \(5=n+3\), then \(n+3=\) ? (Symmetric property of equality)

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(-2(x+4)-(2 x-1), x=-3\)

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

Simplify each numerical expression. $$9-12-8+5-6$$

Simplify each of the numerical expressions. $$16+9-4-2+8-1$$

Evaluate the algebraic expressions in Problems 35-57 for the given values of the variables. \(-4(2 x-1)+7(3 x+4), \quad x=4\)

Simplify each of the numerical expressions. $$4(0.1)^{2}-6(0.1)+0.7$$

Simplify each numerical expression. $$6-9+11-8-7+14$$

Simplify each of the numerical expressions. $$18+17-9-2+14-11$$

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