1-8 An Introduction to Equations

Quick Review

An equation can be true or false, or it can be an open sentence with a variable. A solution of an equation is the value (or values) of the variable that makes the equation true.

Example

Is c = 6 a solution of the equation 25 = 3 c − 2 ? 25 equals 3 bold italic c minus 2 question mark

25 = 3 c − 2   25 = ? 3 · 6 − 2 Substitute  6  for  c . 25 ± 16 Simplify. table with 3 rows and 2 columns , row1 column 1 , 25 equals 3 c minus 2 , column 2 , row2 column 1 , 25 , modified equals with question mark above , 3 middle dot 6 minus 2 , column 2 cap substitute . 6 , for , c . , row3 column 1 , 25 plus minus 16 , column 2 cap simplify. , end table

No, c = 6 is not a solution of the equation 25 = 3 c − 2 . 25 equals 3 c minus 2 .

Exercises

Tell whether the given number is a solution of each equation.

87. 17 = 37 + 4f; f = − 5 f equals negative 5
88. − 3 a 2 = 27 ; negative 3 , eh squared , equals 27 semicolon  a = 3
89. 3 b − 9 = 21 ; b = − 10 3 b minus 9 equals 21 semicolon b equals negative 10
90. − 2 b + 4 = 3 ; b = 1 2 negative 2 b plus 4 equals 3 semicolon b equals , 1 half

Use a table to find or estimate the solution of each equation.

91. x + ( − 2 ) = 8 x plus open negative 2 close equals 8
92. 3 m − 13 = 24 3 m minus 13 equals 24
93. 4 t − 2 = 9 4 t minus 2 equals 9
94. 6 b − 3 = 17 6 b minus 3 equals 17

1-9 Patterns, Equations, and Graphs

Quick Review

You can represent the relationship between two varying quantities in different ways, including tables, equations, and graphs. A solution of an equation with two variables is an ordered pair (x, y) that makes the equation true.

Example

Bo makes $15 more per week than Sue. How can you represent this with an equation and a table?

First write an equation. Let b = Bo's earnings and s = Sue's earnings. Bo makes $15 more than Sue, so b = s + 15. You can use the equation to make a table for s = 25, 50, 75, and 100.

Exercises

Tell whether the given ordered pair is a solution of each equation.

95. 3x + 5 = y; (1, 8)
96. y = − 2 ( x + 3 ) ; ( − 6 , 0 ) y equals negative 2 open x plus 3 close semicolon open negative 6 comma 0 close
97. y = ( x − 1.2 ) ( − 3 ) ; y equals open x minus 1.2 close open negative 3 close semicolon  (0, 1.2)
98. 10 − 5 x = y ; ( − 4 , 10 ) 10 minus 5 x equals y semicolon open negative 4 comma 10 close
99. Describe the pattern in the table using words, an equation, and a graph. Extend the pattern for x = 5, 6, and 7.

    x	y
    1	15
    2	25
    3	35
    4	45

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