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

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

Practice Questions Answers and Explanations

      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.

      5 The numbers 11 and 3 are prime. Yes, appears again!

      6 The only imaginary number is or .

      7

      The points 0.5 and 3.2 are approximated, because the tick marks aren’t on the number line.

      8

      9 3. There are three terms. The term 4x is separated from 3x³ by subtraction and from 11 by addition.

      10 5. There are two terms, and each has a different number of factors. The first term, 3xy, has three factors: the 3 and the x and the y are multiplied together. The second term, 2z, has two factors, the 2 and the z. So there are a total of five factors.

      11 x and y; h, k, a, b, 1. The two variables are x and y. The constants are h, k, a, b, and 1.

      12 2, , and 1. The exponent in the term z² is the 2; the z is the base. The exponent in z^1/2 is . And, even though it isn’t showing, there’s an implied exponent in the term z; it’s assumed to be a 1, and the term can be written as z¹.

      13 . You could put the dot between the 4 and the z to indicate multiplication, but writing them together assumes they’re being multiplied.

      14 . Use a fraction to indicate multiplication, rather than the slash.

      15 . Writing the 6 next to the absolute value indicates multiplication. The subtraction is written completely under the radical.

      16 .

      17 or .

18 The braces contain two terms: the 16 and the fraction. The 5 in front of the braces indicates that multiplication will be performed. The fraction line has the term in the numerator and the number 12 in the denominator. And the parentheses have a multiplier of 4 in front and the two terms 11 and z inside, which need to be subtracted.

      19 . The 9 can be written behind or in front of the parentheses.

      20 . The x goes in the denominator.

      21 . Use parentheses if the –2 follows the x.

      22