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Apa 6th Edition
Beginning And Intermediate Algebra 6th Edition free. download full
Sample questions asked in the 6th edition of Beginning & Intermediate Algebra:
Write the fraction as an equivalent fraction with the given denominator. See Example 6. EXAMPLE 6 Write as an equivalent fraction with a denominator of 20. Solution Since 5 · 4 = 20, multiply the fraction by . Multiplying by does not change the value of the fraction. Thus, with a denominator of 9
A 21-foot beam is to be cut into three pieces so that the second and the third piece are each 3 times the length of the first piece. If x represents the length of the shorter piece, find the lengths of all three pieces.
Solve the system of equations by the substitution method. See Examples 1 through 6 . EXAMPLE 1 Solve the system: Solution The second equation in this system is x = y + 2. This tells us that x and y + 2 have the same value. This means that we may substitute y + 2 for x in the first equation. Notice that this equation now has one variable, y . Let’s now solve this equation for y . Now we know that the y -value of the ordered pair solution of the system is 2. To find the corresponding x -value, we replace y with 2 in the equation x = y + 2 and solve for x . The solution of the system is the ordered pair (4, 2). Since an ordered pair solution must satisfy both linear equations in the system, we could have chosen the equation 2 x + y = 10 to find the corresponding x -value. The resulting x -value is the same. Check: We check to see that (4, 2) satisfies both equations of the original system. The solution of the system is (4, 2). A graph of the two equations shows the two lines intersecting at the point (4, 2). EXAMPLE 2 Solve the system: Solution The second equation is solved for y in terms of x . We substitute 3 x for y in the first equation. Now we solve for x . The x -value of the ordered pair solution is ?1. To find the corresponding y -value, we replace x with ?1 in the second equation, y = 3 x . Check to see that the solution of the system is (?1, ?3). EXAMPLE 3 Solve the system: Solution We choose one of the equations and solve for x or y . We will solve the first equation for x by subtracting 2 y from both sides. Since x = 7 ? 2 y , we now substitute 7 ? 2 y for x in the second equation and solve for y . To find x , we let in the equation x = 7 ? 2 y . The solution is . Check the solution in both equations of the original system. EXAMPLE 4 Solve the system: Solution To avoid introducing fractions, we will solve the second equation for y . Next, substitute 3 x + 6 for y in the first equation. To find the corresponding y -value, substitute ?2 for x in the equation y = 3 x + 6. Then y = 3(?2) + 6 or y = 0. The solution of the system is (?2, 0) . Check this solution in both equations of the system. EXAMPLE 5 Solve the system: Solution The second equation is already solved for x in terms of y . Thus we substitute 6 + 2 y for x in the first equation and solve for y . Arriving at a true statement such as 3 = 3 indicates that the two linear equations in the original system are equivalent. This means that their graphs are identical and there is an infinite number of solutions of the system. Any solution of one equation is also a solution of the other. For the solution, we can write “infinite number of solutions” or, in set notation, EXAMPLE 6 Use substitution to solve the system. Solution Choose the second equation and solve for y . Now replace y with in the first equation. The false statement 0 = 5 indicates that this system has no solution and is inconsistent. The graph of the linear equations in the system is a pair of parallel lines. For the solution, we can write “no solution” or, in set notation, write { } or ?.
Chegg Staff Review of the Textbook:
In my opinion, Beginning and Intermediate Algebra 6th Edition is an excellent and fulfilling resource for students who seek to learn algebra seriously. The content was organized systematically covering the depth of topics needed to master mathematics and algebra. Many examples available in every chapter of the book make it easy to understand the concepts in depth. The author has taken much care to provide examples in which the reasons are highlighted in blue for a clearer understanding. Practice problems are plentiful throughout the textbook, offering a variety of question types covering a myriad of algebra related concepts. Vocabulary plus readiness problems in every section are helpful before solving the actual exercise problems. Concept check problems in the middle of each section are used to help refresh important ideas.
Real-time problems included and covered should boost interest in the subject matter. The four-step problem-solving strategy (pages 107 - 111) is key for students to enhance problem-solving skills. Graphs are well labeled and highlighted in blue to distinguish values from the coordinate axes. And with graphing calculator support, this book can greatly enhance the both technical skills and practical knowledge enhanced by algebra.
Font size is good with decent page quality, and content presentation is impressive throughout.