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Problem Solving Solutions

Problem solving in math is more than just finding an answer.
Problem solving is a SKILL that includes perseverance and planning , among other things, to help make the math make sense to you.
The greatest mathematicians:
- persist .
- look for counter-examples to disprove themselves.
- ask others to find errors in their work.
- go back and fix it or try again .
Important aspects of problem solving:
- You persevere .
- You appropriately use math tools to assist you.
- You look for efficient ways to solve problems.
- You embrace mistakes and then correct them.
- You make a plan to solve complex problems.
Problem-solving plan for equations:

1. At every instance, ask yourself, “What is happening to the variable ?” and list each response to that question.
2. After your list is complete, draw an arrow going from the bottom of your list to the top.
3. For each item in your list, ask yourself, “What operation will “undo” (be the inverse) it?” and list the inverse operation.

No matter the context, the rules of mathematics, including order of operations and inverse operations, stay the same .

Write a plan to isolate x. Then name the inverse of each step.

$\frac{85}{76} x - 243 = 901 \cdot \frac{85}{76} ↑ \cdot \frac{76}{85} - 243 ↑ + 243$

Find x and circle it
What is happening to x?
x is multiplied by $\frac{85}{76}$
243 is subtracted from the x-term
What operation will “undo” what you wrote down?

Write a plan to isolate x.

$\frac{x}{A B} + E = C D$

$\div A B ↑ \cdot A B + E ↑ - E$

Write a plan to isolate x.

$- 3 - \frac{4}{7} x + P = 6$

$\cdot (- \frac{4}{7}) ↑ \cdot (- \frac{7}{4}) - 3 ↑ + 3 + P ↑ - P$