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| Introduction to Solving Equations |
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| 1) For the equation, 5x – 1 = 3x – 15, what three properties were used to determine that x = –7? Name the properties in the order the occurred in the steps. |
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| 2) For the equation, 3(2x + 5) = 9 + 3x, what two properties were used to verify that “x = –2” is the solution of the equation? Name the properties in the order they occurred in the steps. |
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Solving Simple Equations
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| Direct Variation - A Special Case of a Linear Equation |
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| In the following problems, if y varies directly as x, find the constant of variation, and then write an equation of direct variation (y = k x) that relates the two variables. |
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| 16) If y varies directly with x, use the data below to find a formula for this relationship and to complete the table. State the missing numbers in the table in the order in which they occur, and then state the formula. |
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17) Shown below is a graph of a direct-variation equation.
(a) What is the constant of variation?
(b) What is the direct-variation equation?
(c) What is the slope of the line? |
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| Use this scenario to solve the following problems: 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. |
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| Using Equations to Solve Problems |
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| In the following problems, determine what x represents in the problem, write an equation for the conditions of the problem, and then solve. For each problem, state what x represents, state the equation, and then state the answer. |
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| 20) The length of a rectangle is 5 feet more than three times the width. The perimeter of the rectangle is 146 feet. What is the width and the length of the rectangle? State what x represents, state the equation, and then state the answer. |
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| 21) James has 4 test scores of 82, 77, 75 and 84. What score does James need on the next test to have an average of 80? State what x represents, state the equation, and then state the answer. |
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| 22) A store can purchase shirts for $7 each. Each shirt is sold for $18. If the store wants to make a profit of $748, how many shirts must it sell? State what x represents, state the equation, and then state the answer. |
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| 23) It takes a bus 6 hours to take a trip. The train takes only 4 hours to make the same trip. The train travels at a rate of speed that is 25 mph more than the speed of the bus. What is the rate of the bus and the rate of the train? State what x represents, state the equation, and then state the answer. |
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24) Two trains leave from the same station at the same time and travel in opposite directions. One train travels at an average rate of 50 mph, the other at 70 mph. In how many hours will they be 330 miles apart? State what x represents, state the equation, and then state the answer.
Hint: Set up a table to organize the information. (Note: The trains are traveling at different rates; but, the time they travel to reach 330 miles apart will be the same.) |
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| 25) How many liters of a 40% acid solution should be mixed with 8 liters of a 25% acid solution to obtain a solution that is 30% acid? State what x represents, state the equation, and then state the answer. |
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| 26) Working alone, a painter can paint a living room in 6 hours. A second painter can do the job in 9 hours. How long will it take them to paint the room if they work together? State what x represents, state the equation, and then state the answer. |
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| In the following problems, solve the formula for the given variable. |
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| 27) Solve I = prt for r. |
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| 28) Solve the formula for g. |
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| 29) The formula for the perimeter of a rectangle is P = 2l + 2w. Solve the formula for l. Then use the new formula to find the length of a rectangle if the perimeter is 68 feet and the width is 14 feet. State the new formula and the length of the rectangle. |
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| 30) If you were directed by your school to complete Offline Activities for this course, please enter the information on the Log Entry form. |
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