1. Opener:
Decide if each operation is reversible. If it is, give the number
used and explain how you reversed the operation. If it isn't
reversible, give a counterexample to support your answer.
1. Mary found the sum of the digits in a number to be 6.
What number was she using?
2. Robert squared a number and got 81. What was his
number?
3. Jeffrey square rooted a number and got 3. What was
his number?
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2. Partner Practice: Complete the problems below with your partners.
1. Write each expression as a number trick. If
the number trick is reversible, describe the
operations that reverse it in the correct order.
a. 3(5m ‐ 12)
b. 15m ‐ 36
2. Hidecki says, "I take a number, multiply it by 12,
and then subtract 9. My final result is ‐5." What is
Hidecki's starting number? (List the steps to
reverse this number trick and then apply the steps
to the final number.)
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4. Section 2.8 Solving Equations by Backtracking
Moving to Algebra:
What is an equation?
A mathematical sentence that states that two
quantities are equal.
Equations are not necessarily true.... Are these equations
true or false?
1. 2 + 5 = 7 ________
2. 3 + 8 = 10 ________
3. x + y = y + x ________
4. x = x + 1 ________
5. x + 1 = 8 ________
When equation are sometimes true and sometimes false,
the values of the variable which make the equation true
are called the solutions of the equation.
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5. More about Solutions: Example 1: Why is the value 3 a solution to the
equation x + 4 = 7?
Example 2: Is the number 7 a solution to the
equation 3x ‐ 28 = 46? Why or why not?
Example 3: Can you find a solution to the equation
3x ‐ 28 = 46 by backtracking? (Think of it as a
number trick.)
Number Trick Steps Backtracking Steps
Example 4: Show that x = 1 and x = 8 are solutions to the
equation x3 + 26x = 11x2 + 16.
Can you come up with two numbers that are not solutions?
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6. Use Backtracking: Solve the following equations by Backtracking!
1. 2x ‐ 7 = 110
2. 38 = 5n ‐ 1
3.
4.
5. 3(a ‐ 1) ‐ 5 = 34
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