Solve each of these equations. Explain or show your reasoning.
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1.
2(x + 5) = 3x + 1
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2.
3y - 4 = 6 - 2y
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3.
3(n + 2) = 9(6 - n)
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4.
Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Clare’s mistake and what is the solution to the equation?
12(5 + 2y) = 4y - (5 - 9y)
72 + 24y = 4y - 5 - 9y
72 + 24y = -5y - 5
24y = -5y -77
29y = -77
y = -77/29
Solve each equation, and check your solution.
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5.
1/9(2m - 16) = 1/3(2m +4)
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6.
-4(r + 2) = 4(2 - 2r)
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7.
12(5 + 2y) = 4y - (6 - 9y)
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8.
Here is the graph of a linear equation.
Select all true statements about the line and its equation.
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9.
A participant in a 21-mile walkathon walks at a steady rate of 3 miles per hour. He thinks, “The relationship between the number of miles left to walk and the number of hours I already walked can be represented by a line with slope -3.” Do you agree with his claim? Explain your reasoning.