1. Consider first a linear equation: 3x â 1 = 5.
a. Use a graphing utility to show y1= 2x â 1 and y2=5 and determine the point of intersection. Make a sketch and label it.
b. How does the graph in part (a) relate to the solution set of the equation 3x â 1 = 5?
c. To solve the equation 3x â 1 =5 algebraically, the first step is to add 1 to both sides of the equation. Use a graphing utility to show y1=3x and y2=6, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation 3x=6?
d. The final step to solve the equation is to divide both sides of the equation by 3. Use a graphing utility to show y1=x and y2=2, and determine the point of intersection. Make a sketch and label it. How does this graph relate to the equation x=2?
e. The algebraic steps to solve the equation 3x â 1 = 5 produce two equations: 3x=6 and x=2. How do the graphs you sketched above represent the fact that these equations are equivalent to the original?
CHAPTER INQuIRY . BASED LEARNING PROJECT A general stratey forsolving all the various types of equations you encountered in this chapter can be sunmarized as follows From a given equation, partom agebraic operations on both sides in order to gonorate equivalent equations Remember 1. Consider fiest a linear equation 3-1-5 of intersection Make a sketch and label t. ar-1- 51 c To soive the equation 3r-1-5algebraically, the firnt step is to add 1 to both des of equation blows Use a graphing utility to show -3r and - & and determine the point of intersection. Make a sketch and isbel t. How dows tie graph relate to the equation 3r- 0? dThe final algebrac otep to solo eqatan i. to divide boh sides of equation by 3 Use a graphing utility to show y -r and y-2, and determine the point of intersection Make a sketch and label t How does this graph relate to the equationã 2? a The algebraic steps to sdve the equation 3-1-5 produce two equations 3r- 6 and-2 How do the graphe you sketched above represent the fact that tese egations·e equivalent to tho ongna?
