is subtracted from 3 times y.
2. Add 2 and y; then divide that sum by 11.
Practice Answers
1.
2.
Defining relationships
Algebra is all about relationships – not the he-loves-me-he-loves-me-not kind of relationship – but the relationships between numbers or among the terms of an expression. Although algebraic relationships can be just as complicated as romantic ones, you have a better chance of understanding an algebraic relationship. The symbols for the relationships are given here. The equations are found in Chapters 14 through 18, and inequalities are found in Chapter 19.
✓ = means that the first value is equal to or the same as the value that follows.
✓ ≠ means that the first value is not equal to the value that follows.
✓ means that one value is approximately the same or about the same as the value that follows; this is used when rounding numbers.
✓ ≤ means that the first value is less than or equal to the value that follows.
✓ < means that the first value is less than the value that follows.
✓ ≥ means that the first value is greater than or equal to the value that follows.
✓ > means that the first value is greater than the value that follows.
Practice Questions
Write the expression using the correct symbols.
1. When you multiply the difference between z and 3 by 9, the product is equal to 13.
2. Dividing 12 by x is approximately the cube of 4.
3. The sum of y and 6 is less than the product of x and –2.
4. The square of m is greater than or equal to the square root of n.
Practice Answers
1. (z – 3)9 = 13 or 9(z – 3) = 13. The 9 can be written behind or in front of the parentheses.
2.
3. y + 6 < –2x or y + 6 < x(–2). Use parentheses if the –2 follows the x.
4.
Taking on algebraic tasks
Algebra involves symbols, such as variables and operation signs, which are the tools that you can use to make algebraic expressions more usable and readable. These things go hand in hand with simplifying, factoring, and solving problems, which are easier to solve if broken down into basic parts. Using symbols is actually much easier than wading through a bunch of words.
✓ To simplify means to combine all that can be combined, cut down on the number of terms, and put an expression in an easily understandable form.
✓ To factor means to change two or more terms to just one term using multiplication. (See Chapters 11 through 13 for more on factoring.)
✓ To solve means to find the answer. In algebra, it means to figure out what the variable stands for. (You see solving equations and inequalities in Chapters 14 through 19.)
Equation solving is fun because there’s a point to it. You solve for something (often a variable, such as x) and get an answer that you can check to see whether you’re right or wrong. It’s like a puzzle. It’s enough for some people to say, “Give me an x.” What more could you want? But solving these equations is just a means to an end. The real beauty of algebra shines when you solve some problem in real life – a practical application. Are you ready for these two words: story problems? Story problems are the whole point of doing algebra. Why do algebra unless there’s a good reason? Oh, I’m sorry – you may just like to solve algebra equations for the fun alone. (Yes, some folks are like that.) But other folks love to see the way a complicated paragraph in the English language can be turned into a neat, concise expression, such as, “The answer is three bananas.”
Going through each step and using each tool to play this game is entirely possible. Simplify, factor, solve, check. That’s good! Lucky you. It’s time to dig in!
Chapter 2
Deciphering Signs in Expressions
In This Chapter
Numbers have many characteristics: They can be big, little, even, odd, whole, fraction, positive, negative, and sometimes cold and indifferent. (I’m kidding about that last one.) Chapter 1 describes numbers’ different names and categories. But this chapter concentrates mainly on the positive and negative characteristics of numbers and how a number’s sign reacts to different manipulations. This chapter tells you how to add, subtract, multiply, and divide signed numbers, no matter whether all the numbers are all the same sign or a combination of positive and negative.
Positive numbers are greater than 0. They’re on the opposite side of 0 from the negative numbers. If you were to arrange a tug-of-war between positive and negative numbers, the positive numbers would line up on the right side of 0. Negative numbers get smaller and smaller, the farther they are from 0. This situation can get confusing because you may think that –400 is bigger than –12. But just think of –400°F and –12°F. Neither is anything pleasant to think about, but –400°F is definitely less pleasant – colder, lower, smaller.
Remember: When comparing negative numbers, the number closer to 0 is the bigger or greater number. You may think that identifying that 16 is bigger than 10 is an easy concept. But what
