Problem Solving for Unknown Numbers

Solve |x – 12| - 3 = 11.

• x = -2, -26

• x = -2, 26

• x = 3, 25

• x = 4, -7

Solve for r.

−2|−2r − 4| = -12

• r = 5,1

• r = -5,-1

• r = -5,1

• No Solution

|3m - 9| = 18

• m = 9,-3

• m = 9,3

• m = 9

• no solution

|d + 3| = 6 - 2d

• d = 1, 9

• d = -1

• d = 1

• no solution

2|a - 5| = 22

• a = 16

• a = 16, -6

• a = 16, 6

• no solution

|3h + 2| = 14 - h

• h = 3, -8

• h = 3

• h = 3, 8

• no solution

If a problem asks “how many cubes are in the nth figure,” an approach to solving the problem might be:

• Guess and Test.

• Draw a Picture.

• Make a Table.

• Look for a Pattern.

• Use a Variable.

If you are given a sequence of numbers and asked to predict the next number in the sequence, a problem solving strategy you might reasonably try is

• Look for a Pattern.

• Draw a Picture.

• Guess and Test.

• Trial and Error.

• None of these is a particularly good strategy.

When using the Guess and Test Problem Solving Strategy you will probably be most successful if you

• a. simply try possibilities at random.

• b. use a means of organizing your guesses.

• c. try to learn from each of the trials.

• d. apply both parts (a) and (c).

• e. apply both parts (b) and (c).

If a problem asks you to “Find a formula . . . “ you might begin by

• drawing a sketch of the problem situation.

• understanding the terms used in the problem.

• looking for relationships between known quantities and the unknown quantity.

• making a tables of values, using n as the unknown quantity.

• trying any one of the above.