Lesson 6
Strategic Solving
Problem 1
Solve each of these equations. Explain or show your reasoning.
\(2b+8-5b+3=\text-13+8b-5\)
\(2x+7-5x+8=3(5+6x)-12x\)
\(2c-3=2(6-c)+7c\)
Solution
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Problem 2
Solve each equation and check your solution.
\(\text-3w-4=w+3\)
\(3(3-3x)=2(x+3)-30\)
\(\frac13(z+4)-6=\frac23(5-z)\)
Solution
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Problem 3
Elena said the equation \(9x+15=3x+15\) has no solutions because \(9x\) is greater than \(3x\). Do you agree with Elena? Explain your reasoning.
Solution
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Problem 4
The table gives some sample data for two quantities, \(x\) and \(y\), that are in a proportional relationship.
- Complete the table.
- Write an equation that represents the relationship between \(x\) and \(y\) shown in the table.
- Graph the relationship. Use a scale for the axes that shows all the points in the table.
| \(x\) | \(y\) |
|---|---|
| 14 | 21 |
| 64 | |
| 39 | |
| 1 |
Solution
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(From Unit 3, Lesson 3.)