Page 617 - Basic College Mathematics with Early Integers

594 C HAPTE R 8 I INTRODUCTION TO ALGEBRA

Concept Extensions

Using the steps for solving an equation, choose the next operation for solving the given equation.

97. 2x - 5 =-7 98. 3x + 2x =-x - 4
a. Add 7 to both sides. a. Add 4 to both sides.
b. Add 5 to both sides. b. Subtract 2x from both sides.
c. Divide both sides by 2. c. Add 3x and 2x.

99. -3x =-12 100. 9 - 5x = 15
a. Divide both sides by -3. a. Divide both sides by -5.
b. Add 12 to both sides. b. Subtract 15 from both sides.
c. Add 3x to both sides. c. Subtract 9 from both sides.

A classmate shows you steps for solving an equation.The solution does not check, but the classmate is unable to find the
error. For each set of steps, check the solution, find the error, and correct it.

101. 2(3x - 5) = 5x - 7 102. 37x + 1 = 914x - 72
6x - 5 = 5x - 7 37x + 1 = 36x - 7
6x - 5 + 5 = 5x - 7 + 5 37x + 1 - 1 = 36x - 7 - 1
6x = 5x - 2 37x = 36x - 8
6x - 5x = 5x - 2 - 5x 37x - 36x = 36x - 8 - 36x
x =-2 x =-8

Solve.

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103. (-8) + 3x = 5x + 4 3 104. 3 2 # x = (-9) 3

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105. 2 (x + 4) = 3 (x + 4) 106. x + 45 = 54 2
107. A classmate tries to solve 3x = 39 by subtracting 108. A classmate tries to solve 2 + x = 20 by dividing
3 from both sides of the equation.Will this step both sides by 2.Will this step solve the equation
solve the equation for x? Why or why not? for x? Why or why not?

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The equation C = 1F - 322 gives the relationship between Celsius temperatures C and Fahrenheit temperatures F.
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109. The highest recorded temperature in Australia 110. The highest recorded temperature in Africa
occurred in January 1960 at Oodnadatta, South occurred in September 1922 at Al’Aziziyah, Libya.
Australia.The temperature reached 50.7°C. Use the The temperature reached 57.8°C. Use the given
given equation to convert this temperature to equation to convert this temperature to degrees
degrees Fahrenheit. (Source: World Weather Centre Fahrenheit. (Source: World Weather Centre at
at Perth) Perth)

111. The lowest recorded temperature in Australia 112. The lowest recorded temperature in North America
occurred in June 1994 at Charlotte Pass, New South occurred in February 1947 at Snag, Canada.The
Wales.The temperature plummeted to -23.0°C. Use temperature plummeted to -63.0°C. Use the given
the given equation to convert this temperature to equation to convert this temperature to degrees Copyright 2012 Pearson Education, Inc.
degrees Fahrenheit. (Source: World Weather Centre Fahrenheit. (Source: World Weather Centre at Perth)
at Perth)