Victory for the ACT Student Text 15e

L ESSON 2 | A LGEBRA AND F UNCTIONS • 219

SOLVING ALGEBRAIC EQUATIONS OR INEQUALITIES WITH ONE VARIABLE

If ( ) ( ) x 2 3 1 1

, then x

?

If − , which of the following †‡ϐ‹‡• –Š‡ ’‘••‹„Ž‡ ˜ƒŽ—‡• ˆ‘” x ? F. x 20 G. x 0 ! H. x 2 ! J. < x 0 20 K. <

+ + =

Simple Equations Item #19

19.

24.

25

A. B.

5

Throwback to Math Class Remember to solve for a variable means to isolate that variable. The general technique is to get the variable alone on one side with all other terms on the other side of the equation. Throwback to Math Class Manipulating inequalities is the same as manipulating equations except you have an inequality symbol, and whenever you multiply or divide by a negative number you must ϐŽ‹’ –Š‡ •‹‰Ǥ Simple Inequalities Item #20 Equations Involving Rational Expressions Items #21–23 Inequalities Involving Rational Expressions Item #24

4 1 C. 1 D. 4 E. 5

20. If x 2 3 9 >+ , which of the following can be the value of x ? F. –4 G. –3 H. 0 J. 3 K. 4 21. If x 1 12 1 2 + − = , and x 1 ! , then x ? A. 1 B. 2 C. 3 D. 11 E. 12

Rewrite the terms using a common denominator and factor it out of the equation. Do not transpose multiplicative factors involving x . Solving for x gives a range of values with an upper or lower limit. Check this range for values of x that make the denominator zero or that change the sign of the rational expression. If necessary, further limit the possible range to exclude these values.

Step 2:

If

, and x

, then x

?

2 !

x

3

=

22.

+

x

2 4 F. 6 G. 4 H. 3 J. 2 K. 1

If 2 ! , which of the following is the complete solution set for x ( 2 2 2 ) x x x x 2 8 − − − + = , and x

23.

? A. {} B. { }2 C. { }2 D. { }4 E. { }8