Questions

For the first four problems, if “y varies directly as x”, find the constant of variation and write an equation of direct variation that relates the two variables.

1) y = 21, when x = 7

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2) Find the constant of variation and write an equation.

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3) y = 0.4 when x = –1

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4) Find the constant of variation and write an equation.

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For the next six problems, solve each equation for the unknown.

5) 3x – 5 = 15

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6) –2x + 7 = 29

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7) 5(x + 3) = –45

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8) Solve for “x”.

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9) 3(m – 2) – 5 = 6 – 2(m – 4)

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10) Solve for “m”.

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For the next four problems, solve each proportion.

11) Solve for “x”.

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12) Solve for “x”.

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13) Solve for “x”.

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14) Solve for “x”.

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15) At a given time, the height of an object is directly proportional to the length of the shadow that is cast on the ground. A person 6 feet tall casts a shadow 1 foot long at noon. a) What is the length of the shadow cast by a flagpole known to be 20 feet tall? b) A tree cast a shadow of 3 feet. How tall is the tree?

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For the next seven problems, state the property that matches the example. Choose from the list of properties below.

16) If a = b, then a + c = b + c.

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17) State the property.

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18) a = a

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19) If a = b, then b = a.

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20) If a = b, then a – c = b – c.

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21) If a = b and b = c, then a = c.

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22) If a = b, then ac = bc.

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23) Solve 5x – 1 = 3x – 15. Explain each step, and include the Properties of Equality that you used.

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24) Explain how to verify that 3(2x + 5) = 9 + 3x and x = –2 are equivalent equations.

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