Answers to problem 6-29: a: , b: , c:
Rewriting equations with more than one variable may be done in a variety of ways but normally you follow the same steps as you would for solving an equation with a single variable. Commonly, the first step is to multiply all the terms by a common denominator to remove all of the fractions. Then solve in the usual way. Collect like terms. Isolate the specified variable terms on one side and everything else on the other. Finally, divide or undo the exponent so that the variable is alone. The final answer will be an equation that involves variables and possibly numbers.
Example 1: Solve for y:
Solution: 2x + 3y − 9 = 0
subtract, add on each side
3 divide by 3
Example 2: Solve for r: V =πr3
Solution: V =πr3
3V = 4πr3
multiply by 3 on each side
Now we can go back and solve the original problems.
Here are some more to try. Solve each equation for the specified variable.
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This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.
Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.