Use the equation to complete parts (a) through (c). Build the equation on your Equation Mat using and simplify it as much as possible. Record your steps and what you see when you have simplified the equation fully. Draw a picture of your final mat. Have each member of your team test a different value for in the original equation, such x as = 0, = 1, = = 10, etc. What happens in each case? x x x x −5, Are any solutions to this equation? If so, how many? SPECIAL CASES, Part Two Use the equation to complete parts (a) through (c). Build the equation on your Equation Mat using and simplify it as much as possible. Record your steps and what you see when you have simplified the equation fully. Draw a picture of your final mat. Have each member of your team test a different value for in the equation, such as = x x 0, = 1, = = 10, etc. What happens? Is there a pattern to the results you get from the x x x −5, equation? Did you find any values for that satisfied the equation in part (a)? When is an x imbalance of units left on the mat (such as 2 = 0), what does this mean? Is = 0 a solution x to the equation? Keeping these special cases in mind, continue to develop your equation-solving strategies by visualizing and solving each equation below. Remember to build each equation on your mat, if needed, to simplify as much as possible, and to solve for Identify if one number is x. the solution, if any number is the solution, or if there is no solution. Record your steps. Additional Challenge: For each of the parts below, create your own equation (involving at least three steps) that has the given solution. = x –2 = x no solution all numbers Investigation 13: Choosing a Solving Strategy
Use the equation to complete parts (a) through (c). Build the equation on your Equation Mat using and simplify it as much as possible. Record your steps and what you see when you have simplified the equation fully. Draw a picture of your final mat. Have each member of your team test a different value for x in the original equation, such as x = 0, x = 1, x = −5, x = 10, etc. What happens in each case? Are any solutions to this equation? If so, how many? SPECIAL CASES, Part Two Use the equation to complete parts (a) through (c). Build the equation on your Equation Mat using and simplify it as much as possible. Record your steps and what you see when you have simplified the equation fully. Draw a picture of your final mat. Have each member of your team test a different value for x in the equation, such as x = 0, x = 1, x = −5, x = 10, etc. What happens? Is there a pattern to the results you get from the equation? Did you find any values for x that satisfied the equation in part (a)? When is an imbalance of units left on the mat (such as 2 = 0), what does this mean? Is x = 0 a solution to the equation? Keeping these special cases in mind, continue to develop your equation-solving strategies by visualizing and solving each equation below. Remember to build each equation on your mat, if needed, to simplify as much as possible, and to solve for x. Identify if one number is the solution, if any number is the solution, or if there is no solution. Record your steps. Additional Challenge: For each of the parts below, create your own equation (involving at least three steps) that has the given solution. x = –2 x = no solution all numbers Investigation 13: Choosing a Solving Strategy
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