Mary Jane Sterling - Algebra I All-in-One For Dummies

A. . The wavy equal sign means “approximately” or “about.”

Write the expression using the correct symbols.

19 When you multiply the difference between z and 3 by 9, the product is equal to 13.

20 Dividing 12 by x is approximately the cube of 4.

21 The sum of y and 6 is less than the product of x and –2.

22 The square of m is greater than or equal to the square root of n .

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, using allowable operations, to cut down on the number of terms, and to 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 11through 13for more on factoring.)

To solve means to find the answer. In algebra, it means to figure out what the variable stands for. You solve for the variable to create a statement that is true. (You see solving equations and inequalities in Chapters 14through 19.)

To check your answer means to replace the variable with the number or numbers you have found when solving an equation or inequality, and show that the statement is true.

Q. Simplify the expression:

A.You can add the two numbers. Simplified, you get . You see all the types of simplifying methods in Chapter 7.

Q. Factor the expression:

A.The two terms have a common factor of 5. Make this one term by taking out the common factor and writing it times the sum of the remaining factors. This can be or, simplifying, it’s . Factoring methods are found in Chapters 11through 13.

Q. Solve the equation for the value of x : .

A.The only number that will make this equation a true statement is the number 3. So . Solving equations is covered in Chapters 14through 18.

Q. Check to see if it’s true that in the equation .

A.Replace the x in the equation and simplify on the left. You have , which is the same as or . Yes, this is the solution to the equation.

23 Simplify the expression .

24 Factor the expression .

25 Solve for the value of z in the equation .

26 Check to see if both and 3 are solutions to the equation .

1 The numbers 15, 11, and are natural numbers.The number qualifies, because it simplifies to the number 3.

2 The numbers –41, 15, 11, , and are integers.The fraction simplifies to , and is equal to 3.

3 The numbers are all rational numbers.

They can all be written as a fraction with integers in the numerator and denominator.

4 The number is the only irrational number listed here.Technically, can be written as , but the i makes the number imaginary. And the can be simplified to create a rational number.