11.8: Exercise Supplement

Algebraic Expressions

For problems 1-10, specify each term.

Exercise \(\PageIndex{1}\)

\(6a - 2b + 5c\)

Answer

\(6a, -2b, 5c\)

Exercise \(\PageIndex{2}\)

\(9x - 6y + 1\)

Exercise \(\PageIndex{3}\)

\(7m - 3n\)

Answer

\(7m, -3n\)

Exercise \(\PageIndex{4}\)

\(-5h + 2k - 8 + 4m\)

Exercise \(\PageIndex{5}\)

\(x + 2n - z\)

Answer

\(x, 2n, -z\)

Exercise \(\PageIndex{6}\)

\(y - 5\)

Exercise \(\PageIndex{7}\)

\(-y - 3z\)

Answer

\(-y, -3z\)

Exercise \(\PageIndex{8}\)

\(-a - b - c - 1\)

Exercise \(\PageIndex{9}\)

\(-4\)

Answer

\(-4\)

Exercise \(\PageIndex{10}\)

\(-6\)

Exercise \(\PageIndex{11}\)

Write \(1k\) in a simpler way.

Answer

\(k\)

Exercise \(\PageIndex{12}\)

Write \(1x\) in a simpler way.

Exercise \(\PageIndex{13}\)

In the expression \(7r\), how many \(r\)'s are indicated?

Answer

7

Exercise \(\PageIndex{14}\)

In the expression \(12m\), how many \(m\)'s are indicated?

Exercise \(\PageIndex{15}\)

In the expression \(-5n\), how many \(n\)'s are indicated?

Answer

-5

Exercise \(\PageIndex{16}\)

In the expression \(-10y\), how many \(y\)'s are indicated?

For problems 17-46, find the value of each expression.

Exercise \(\PageIndex{17}\)

\(5a - 2s\), if \(a = -5\) and \(s = 1\)

Answer

-27

Exercise \(\PageIndex{18}\)

\(7n - 3r\), if \(n = -6\) and \(r = 2\)

Exercise \(\PageIndex{19}\)

\(9x + 2y - 3s\), if \(x = -2\), \(y = 5\), and \(s = -3\)

Answer

1

Exercise \(\PageIndex{20}\)

\(10a - 2b + 5c\), if \(a = 0\), \(b = -6\), and \(c = 8\)

Exercise \(\PageIndex{21}\)

\(-5s - 2t + 1\), if \(s = 2\) and \(t = -2\)

Answer

-5

Exercise \(\PageIndex{22}\)

\(-3m - 4n + 5\), if \(m = -1\) and \(n = -1\)

Exercise \(\PageIndex{23}\)

\(m - 4\), if \(m = 4\)

Answer

0

Exercise \(\PageIndex{24}\)

\(n = 2\), if \(n = 2\)

Exercise \(\PageIndex{25}\)

\(-x + 2y\), if \(x = -7\) and \(y = -1\)

Answer

5

Exercise \(\PageIndex{26}\)

\(-a + 3b - 6\), if \(a = -3\) and \(b = 0\)

Exercise \(\PageIndex{27}\)

\(5x - 4y - 7y + y - 7x\), if \(x = 1\) and \(y = - 2\)

Answer

18

Exercise \(\PageIndex{28}\)

\(2a - 6b - 3a - a + 2b\), if \(a = 4\) and \(b = -2\)

Exercise \(\PageIndex{29}\)

\(a^2 - 6a + 4\), if \(a = -2\)

Answer

20

Exercise \(\PageIndex{30}\)

\(m^2 - 8m - 6\), if \(m = -5\)

Exercise \(\PageIndex{31}\)

\(4y^2 + 3y + 1\), if \(y = -2\)

Answer

11

Exercise \(\PageIndex{32}\)

\(5a^2 - 6a + 11\), if \(a = 0\)

Exercise \(\PageIndex{33}\)

\(-k^2 - k - 1\), if \(k = -1\)

Answer

-1

Exercise \(\PageIndex{34}\)

\(-h^2 - 2h - 3\), if \(h = -4\)

Exercise \(\PageIndex{35}\)

\(\dfrac{m}{6} + 5m\), if \(m = -18\)

Answer

-93

Exercise \(\PageIndex{36}\)

\(\dfrac{a}{8} - 2a + 1\), if \(a = 24\)

Exercise \(\PageIndex{37}\)

\(\dfrac{5x}{7} + 3x - 7\), if \(x = 14\)

Answer

45

Exercise \(\PageIndex{38}\)

\(\dfrac{3k}{4} - 5k + 18\), if \(k = 16\)

Exercise \(\PageIndex{39}\)

\(\dfrac{-6a}{5} + 3a + 10\), if \(a = 25\)

Answer

55

Exercise \(\PageIndex{40}\)

\(\dfrac{-7h}{9} - 7h - 7\), if \(h = -18\)

Exercise \(\PageIndex{41}\)

\(5(3a + 4b)\), if \(a = -2\) and \(b = 2\)

Answer

10

Exercise \(\PageIndex{42}\)

\(7(2y - x)\), if \(x = -1\) and \(y = 2\)

Exercise \(\PageIndex{43}\)

\(-(a - b)\), if \(a = 0\) and \(b = -6\)

Answer

-6

Exercise \(\PageIndex{44}\)

\(-(x - x - y)\), if \(x = 4\) and \(y = -4\)

Exercise \(\PageIndex{45}\)

\((y + 2)^2 - 6(y + 2) - 6\), if \(y = 2\)

Answer

-14

Exercise \(\PageIndex{46}\)

\((a - 7)^2 - 2(a - 7) - 2\), if \(a = 7\)

Combining Like Terms Using Addition and Subtraction

For problems 47-56, simplify each expression by combining like terms.

Exercise \(\PageIndex{47}\)

\(4a + 5 - 2a + 1\)

Answer

\(2a + 6\)

Exercise \(\PageIndex{48}\)

\(7x + 3x - 14x\)

Exercise \(\PageIndex{49}\)

\(-7b + 4m - 3 + 3n\)

Answer

\(-4n + 4m - 3\)

Exercise \(\PageIndex{50}\)

\(-9k - 8h - k + 6h\)

Exercise \(\PageIndex{51}\)

\(-x + 5y - 8x - 6x + 7y\)

Answer

\(-15x + 12y\)

Exercise \(\PageIndex{52}\)

\(6n - 2n + 6 - 2 - n\)

Exercise \(\PageIndex{53}\)

\(0m + 3k - 5s + 2m - s\)

Answer

\(3k + 2m - 6s\)

Exercise \(\PageIndex{54}\)

\(|-8| a + |2| b - |-4| a\)

Exercise \(\PageIndex{55}\)

\(|6| h - |-7| k + |-12| h + |4| \cdot |-5| h\)

Answer

\(38 h - 7k\)

Exercise \(\PageIndex{56}\)

\(|0| a - 0a + 0\)

Equation of the Form \(ax = b\) and \(\dfrac{x}{a} = b\), Translating Words to Mathematical Symbols , and Solving Problems ([link],[link],[link])

For problems 57-140, solve each equation.

Exercise \(\PageIndex{57}\)

\(x + 1 = 5\)

Answer

\(x = 4\)

Exercise \(\PageIndex{58}\)

\(y - 3 = -7\)

Exercise \(\PageIndex{59}\)

\(x + 12 = 10\)

Answer

\(x = -2\)

Exercise \(\PageIndex{60}\)

\(x - 4 = -6\)

Exercise \(\PageIndex{61}\)

\(5x = 25\)

Answer

\(x = 5\)

Exercise \(\PageIndex{62}\)

\(3x = 17\)

Exercise \(\PageIndex{63}\)

\(\dfrac{x}{2} = 6\)

Answer

\(x = 12\)

Exercise \(\PageIndex{64}\)

\(\dfrac{x}{-8} = 3\)

Exercise \(\PageIndex{65}\)

\(\dfrac{x}{15} = -1\)

Answer

\(x = -15\)

Exercise \(\PageIndex{66}\)

\(\dfrac{x}{-4} = -3\)

Exercise \(\PageIndex{67}\)

\(-3x = 9\)

Answer

\(x = -3\)

Exercise \(\PageIndex{68}\)

\(-2x = 5\)

Exercise \(\PageIndex{69}\)

\(-5x = -5\)

Answer

\(x = 1\)

Exercise \(\PageIndex{70}\)

\(-3x = -1\)

Exercise \(\PageIndex{71}\)

\(\dfrac{x}{-3} = 9\)

Answer

\(x = -27\)

Exercise \(\PageIndex{72}\)

\(\dfrac{a}{-5} = 2\)

Exercise \(\PageIndex{73}\)

\(-7 = 3y\)

Answer

\(y = -\dfrac{7}{3}\)

Exercise \(\PageIndex{74}\)

\(-7 = \dfrac{x}{3}\)

Exercise \(\PageIndex{75}\)

\(\dfrac{m}{4} = \dfrac{-2}{5}\)

Answer

\(m = -\dfrac{8}{5}\)

Exercise \(\PageIndex{76}\)

\(4y = \dfrac{1}{2}\)

Exercise \(\PageIndex{77}\)

\(\dfrac{-1}{3} = -5x\)

Answer

\(x = \dfrac{1}{15}\)

Exercise \(\PageIndex{78}\)

\(\dfrac{-1}{9} = \dfrac{k}{3}\)

Exercise \(\PageIndex{79}\)

\(\dfrac{-1}{6} = \dfrac{s}{-6}\)

Answer

\(s = 1\)

Exercise \(\PageIndex{80}\)

\(\dfrac{0}{4} = 4s\)

Exercise \(\PageIndex{81}\)

\(x + 2 = -1\)

Answer

\(x = -3\)

Exercise \(\PageIndex{82}\)

\(x - 5 = -6\)

Exercise \(\PageIndex{83}\)

\(\dfrac{-3}{2} x = 6\)

Answer

\(x = -4\)

Exercise \(\PageIndex{84}\)

\(3x + 2 = 7\)

Exercise \(\PageIndex{85}\)

\(-4x - 5 = -3\)

Answer

\(x = -\dfrac{1}{2}\)

Exercise \(\PageIndex{86}\)

\(\dfrac{x}{6} + 1 = 4\)

Exercise \(\PageIndex{87}\)

\(\dfrac{a}{-5} - 3 = -2\)

Answer

\(a = -5\)

Exercise \(\PageIndex{88}\)

\(\dfrac{4x}{3} = 7\)

Exercise \(\PageIndex{89}\)

\(\dfrac{2x}{5} + 2 = 8\)

Answer

\(x = 15\)

Exercise \(\PageIndex{90}\)

\(\dfrac{3y}{2} - 4 = 6\)

Exercise \(\PageIndex{91}\)

\(m + 3 = 8\)

Answer

\(m = 5\)

Exercise \(\PageIndex{92}\)

\(\dfrac{1x}{2} = 2\)

Exercise \(\PageIndex{93}\)

\(\dfrac{2a}{3} = 5\)

Answer

\(a = \dfrac{15}{2}\)

Exercise \(\PageIndex{94}\)

\(\dfrac{-3x}{7} - 4 = 4\)

Exercise \(\PageIndex{95}\)

\(\dfra{5x}{-2} - 6 = -10\)

Answer

\(x = \dfrac{8}{5}\)

Exercise \(\PageIndex{96}\)

\(-4k - 6 = 7\)

Exercise \(\PageIndex{97}\)

\(\dfrac{-3x}{-2} + 1 = 4\)

Answer

\(x = 2\)

Exercise \(\PageIndex{98}\)

\(\dfrac{-6x}{4} = 2\)

Exercise \(\PageIndex{99}\)

\(x + 9 = 14\)

Answer

\(x = 5\)

Exercise \(\PageIndex{100}\)

\(y + 5 = 21\)

Exercise \(\PageIndex{101}\)

\(y + 5 = -7\)

Answer

\(y = -12\)

Exercise \(\PageIndex{102}\)

\(4x = 24\)

Exercise \(\PageIndex{103}\)

\(4w = 37\)

Answer

\(w = \dfrac{37}{4}\)

Exercise \(\PageIndex{104}\)

\(6y - 11 = 13\)

Exercise \(\PageIndex{105}\)

\(-3x + 8 = -7\)

Answer

\(x = 5\)

Exercise \(\PageIndex{106}\)

\(3z + 9 = -51\)

Exercise \(\PageIndex{107}\)

\(\dfrac{x}{-3} = 8\)

Answer

\(x = -24\)

Exercise \(\PageIndex{108}\)

\(\dfrac{6y}{7} = 5\)

Exercise \(\PageIndex{109}\)

\(\dfrac{w}{2} - 15 = 4\)

Answer

\(w = 38\)

Exercise \(\PageIndex{110}\)

\(\dfrac{x}{-2} - 23 = -10\)

Exercise \(\PageIndex{111}\)

\(\dfrac{2x}{3} - 5 = 8\)

Answer

\(x = \dfrac{39}{2}\)

Exercise \(\PageIndex{112}\)

\(\dfrac{3z}{4} = \dfrac{-7}{8}\)

Exercise \(\PageIndex{113}\)

\(-2 - \dfrac{2x}{7} = 3\)

Answer

\(x = -\dfrac{35}{2}\)

Exercise \(\PageIndex{114}\)

\(3 - x = 4\)

Exercise \(\PageIndex{115}\)

\(-5 - y = -2\)

Answer

\(y = -3\)

Exercise \(\PageIndex{116}\)

\(3 - z = -2\)

Exercise \(\PageIndex{117}\)

\(3x + 2x = 6\)

Answer

\(x = \dfrac{6}{5}\)

Exercise \(\PageIndex{118}\)

\(4x + 1 + 6x = 10\)

Exercise \(\PageIndex{119}\)

\(6y - 6 = -4 + 3y\)

Answer

\(y = \dfrac{2}{3}\)

Exercise \(\PageIndex{120}\)

\(3 = 4a - 2a + a\)

Exercise \(\PageIndex{121}\)

\(3m + 4 = 2m + 1\)

Answer

\(m = -3\)

Exercise \(\PageIndex{122}\)

\(5w - 6 = 4 + 2w\)

Exercise \(\PageIndex{123}\)

\(8 - 3a = 32- 2a\)

Answer

\(a = -24\)

Exercise \(\PageIndex{124}\)

\(5x - 2x + 6x = 13\)

Exercise \(\PageIndex{125}\)

\(x + 2 = 3 - x\)

Answer

\(x = \dfrac{1}{2}\)

Exercise \(\PageIndex{126}\)

\(5y + 2y - 1 = 6y\)

Exercise \(\PageIndex{127}\)

\(x = 32\)

Answer

\(x = 32\)

Exercise \(\PageIndex{128}\)

\(k = -4\)

Exercise \(\PageIndex{129}\)

\(\dfrac{3x}{2} + 4 = \dfrac{5x}{2} = 6\)

Answer

\(x = -2\)

Exercise \(\PageIndex{130}\)

\(\dfrac{x}{3} + \dfrac{3x}{3} - 2 = 16\)

Exercise \(\PageIndex{131}\)

\(x - 2 = 6 - x\)

Answer

\(x = 4\)

Exercise \(\PageIndex{132}\)

\(\dfrac{-5x}{7} = \dfrac{2x}{7}\)

Exercise \(\PageIndex{133}\)

\(\dfrac{2x}{3} + 1 = 5\)

Answer

\(x = 6\)

Exercise \(\PageIndex{134}\)

\(\dfrac{-3x}{5} + 3 = \dfrac{2x}{5} + 2\)

Exercise \(\PageIndex{135}\)

\(\dfrac{3x}{4} + 5 = \dfrac{-3x}{4} - 11\)

Answer

\(x = \dfrac{-32}{3}\)

Exercise \(\PageIndex{136}\)

\(\dfrac{3x}{7} = \dfrac{-3x}{7} + 12\)

Exercise \(\PageIndex{137}\)

\(\dfrac{5y}{13} - 4 = \dfrac{7y}{26} + 1\)

Answer

\(y = \dfrac{130}{3}\)

Exercise \(\PageIndex{138}\)

\(\dfrac{-3m}{5} = \dfrac{6m}{10} - 2\)

Exercise \(\PageIndex{139}\)

\(\dfrac{-3m}{2} + 1 = 5m\)

Answer

\(m = \dfrac{2}{13}\)

Exercise \(\PageIndex{140}\)

\(-3z = \dfrac{2z}{5}\)