Algebra: Form and Function by William G. McCallum, Eric Connally, Deborah Hughes-Hallett

By William G. McCallum, Eric Connally, Deborah Hughes-Hallett

This ebook deals a clean method of algebra that makes a speciality of instructing readers the right way to actually comprehend the foundations, instead of viewing them basically as instruments for different kinds of arithmetic. It depends on a storyline to shape the spine of the chapters and make the cloth extra enticing. Conceptual workout units are integrated to teach how the data is utilized within the genuine global. utilizing symbolic notation as a framework, company pros will come away with a enormously better ability set.

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Dividing both sides by 2 Therefore, the two equations are equivalent. Dividing both sides of an equation by 2 produces an equivalent equation. You can verify that x = 2 is the solution to both equations. (b) The expression 2x + 6 is not equivalent to x + 3. This can be seen by substituting x = 0 into each expression. The first expression becomes 2x + 6 = 2(0) + 6 = 6, but the second expression becomes x + 3 = 0 + 3 = 3. Since 6 is not equal to 3, the expressions are not equivalent. We cannot divide this expression by 2 without changing its value.

4 − 2x) + (5x − 9) 17. (2x)(3y) + 4x + 5y + (6x)(3y) 13. (x + 1) + (x + 2) + (x + 3) 18. (2x)(5x) + (3x)(2x) + 5(3x) + x(3x) PROBLEMS 19. If a + b + c = 12, find the value of 25. The area of a rectangle is 50 square meters. If the length is increased by 25% and the width is increased by 10%, what is the new area? (a + 5) + (b − 3) + (c + 8). 26. Quabbin Reservoir in Massachusetts provides much of Boston’s water. At the start of 2009 the reservoir contained 412 billion gallons of water. 20. If x + y + z = 25, find the value of (y − 10) + (z + 8) + (x − 5).

X = x2 7. s + 10 = 2s 8. 5t = 250 2. The cost for three dinners plus a $5 tip is $32. 3. 80. 4. 60. 9. y − 4 = 3y 12 Chapter 1 THE KEY CONCEPTS OF ALGEBRA In Exercises 10–15, is the value of the variable a solution to the equation? 10. t + 3 = t2 + 9, t = 3 11. x+3 = x2 −9, x = −3 12. x + 3 = x2 − 9, x = 4 13. 14. a+3 a−3 = 1, a = 0 3+a = 1, a = 0 3−a 21. Which of the following are equations? (a) (b) (c) (d) 3(x + 5) = 6 − 2(x − 5) ax2 + bx + c = 0 5(2x − 1) + (5 − x)(x + 3) t = 7(t + 2) − 1 22.

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