Algebra Know-It-ALL
Compare this with the result of the “challenge” problem, where you found out that [(a/b) / (c/d)] / (e/f)=adf / bce Table A-9 i ...
606 Worked-Out Solutions to Exercises: Chapters 1 to 9 Table A-10 shows that the associative property of multiplication holds f ...
We aren’t allowed to get away with trivial solutions, such as letting all the integers be equal to 1 or letting them all be equa ...
608 Worked-Out Solutions to Exercises: Chapters 1 to 9 Here, 100,000 = 105 and 10 = 101. We have 5 − 1, or 4, so there are four ...
The answers, along with explanations, are as follows: (a) We have the number 4-7/10. We can convert the integer part, which is ...
610 Worked-Out Solutions to Exercises: Chapters 1 to 9 repeating sequence in the numerator and a string of 16 digits, all 9s, in ...
Chapter 8 When a negative number is raised to an even positive integer power, the result is always a positive number. When a ne ...
612 Worked-Out Solutions to Exercises: Chapters 1 to 9 When we multiply these out, we get 1/(−2), 1/4, 1/(−8), 1/16, 1/(−32), .. ...
The expression can be simplified to a sum of individual terms when we remember that squaring any quantity (that is, taking it t ...
614 Worked-Out Solutions to Exercises: Chapters 1 to 9 This S/R proof is shown in Table A-11. We can “legally” take the rth pow ...
which simplifies to x2/4. The fraction 2/4 can be reduced to 1/2. That means we actually have x raised to the 1/2 power, or the ...
616 Worked-Out Solutions to Exercises: Chapters 1 to 9 All of these sets are infinite, and the elements of each set can be comp ...
The ratio of the nonnegative square root of 50 to the nonnegative square root of 2 is exactly equal to 5, even though the divide ...
618 Worked-Out Solutions to Exercises: Chapters 1 to 9 The first addend in this expression is ready to go! We can use the distri ...
These worked-out solutions do not necessarily represent the only way a problem can be fig- ured out. If you think you can solve ...
or − 7 =− 7 =− 7 If we multiply an equation through by the number 0, we will always get a statement to the effect that 0 equals ...
We have standard names for the sets of rational and irrational numbers: Q and S, respectively. These sets are disjoint; they ha ...
622 Worked-Out Solutions to Exercises: Chapters 11 to 19 We must simplify the inequality so that y appears all by itself on the ...
If we add 18z to each side, we get z+ 18 z≥− 18 z− 18 + 18 z which simplifies to 19 z≥− 18 We finish by dividing each side by 19 ...
624 Worked-Out Solutions to Exercises: Chapters 11 to 19 We are given the equation x/3+x/6= 12 Multiplying through by 6, we ge ...
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