![]() ![]() We conclude this section by including two more examples similar to those that the student may encounter in other areas. This last equation expresses x in terms of the other symbols. The student will encounter such problems in other courses. Furthermore, (c) is equivalent to (d), therefore (c) has no solution.Īn equation containing more than one variable, or containing symbols representing constants such as a,b, and c, can be solved for one of the symbols in terms of the remaining symbols by applications of the operations T.1 and T.2 in the preceding section. Solving the equation 2x =2+x- 1, we obtain 1 as the only solution Since 1 is not in the replacement of (d), (d) has no solution. Assuming that x!=1, we multiply both sides of (c) by x-1 to obtain The replacement set of (c) is all real numbers except 1. Click on "Solve Similar" button to see more examples. Let’s see how our step by step math solver solves this and similar problems. We now solve as in the previous examples. The next two examples are of equations that reduce to linear equations. Thus each linear equation has at most one solution. Since 2x-3=4+x is equivalent to x-3=4, which, in turn, is equivalent to x=7, whose solution set is obviously, if a!=0. Using these operations we may transform an equation whose solution set is not obvious through a series of equivalent equations to an equation that has an obvious solution set. T.2 The same expression representing a nonzero real number may be multiplied into both sides of an equation. T.1 The same expression representing a real number may be added to both sides of an equation. These operations, sometimes called elementary transformations, are: The following two operations on an equation always result in a new equation which is equivalent to the original one. We define two equations as equivalent if they have the same solution set. In this section we will be concerned with the problem of solving linear equations, and equations that reduce to linear equations. How many steps are needed to solve any equation of the form a x + b = c? Explain.Ĩ8.Equations of the form ax+b=0 are called linear equations in the variable x. ![]() One-half of a number x plus 3 is equal to 10.įind a linear equation of the form a x + b = 0 with the given solution, where a and b are integers. Negative two-thirds times a number x is equal to 20.Ĩ2. Six subtracted from two times a number x is 12.ħ9.ğour added to three times a number n is 25.Ĩ1. The difference of 5 x and 6 is equal to 4.ħ8. Translate the following sentences into linear equations and then solve.ħ4. Is the given value a solution to the linear equation?ġ2. zip file containing this book to use offline, simply click here. You can browse or download additional books there. More information is available on this project's attribution page.įor more information on the source of this book, or why it is available for free, please see the project's home page. Additionally, per the publisher's request, their name has been removed in some passages. ![]() However, the publisher has asked for the customary Creative Commons attribution to the original publisher, authors, title, and book URI to be removed. Normally, the author and publisher would be credited here. This content was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book. See the license for more details, but that basically means you can share this book as long as you credit the author (but see below), don't make money from it, and do make it available to everyone else under the same terms. This book is licensed under a Creative Commons by-nc-sa 3.0 license. ![]()
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