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Grade 8 HMH Go Math - Answer Keys
Chapter 7: Solving Linear Equations; Lesson 4:Equations with Many Solutions or No Solution
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Independent Practice
Tell whether each equation has one, zero, or infinitely many solutions.
Question 7
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\(-(2\text{x} + 2) - 1 = -\text{x} - (\text{x} + 3)\)
Question 8
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\(-2(\text{z} + 3) - \text{z} = -\text{z} - 4 (\text{z} + 2)\)
Create an equation with the indicated number of solutions.
Question 9
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No solution:
\(3(\text{x} - \cfrac{4}{3}) = 3\text{x} + \text{_____}\)
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Question 10
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Infinitely many solutions:
\(2(\text{x} - 1) + 6\text{x} = 4(\text{ _____ } - 1 ) + 2\)
Type below:
Question 11
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One solution of x = -1:
\(5\text{x} - (\text{x} - 2) = 2\text{x} - (\text{ _____ }) \)
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Question 12
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Infinitely many solutions:
\(-(\text{x} - 8) + 4\text{x} = 2(\text{ _____ })+ \text{x}\)
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Question 13
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Persevere in Problem Solving
The Dig It Project is designing two gardens that have the same perimeter. One garden is a trapezoid whose nonparallel sides are equal. The other is a quadrilateral. Two possible designs are shown at the right.
a. Based on these designs, is there more than one value for x? Explain how you know this.
Question 13
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b. Why does your answer to part a make sense in this context?
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Question 13
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c. Suppose the Dig It Project wants the perimeter of each garden to be 60 meters. What is the value of x in this case? How did you find this?