b Solve using the procedures that produce equivalent equations 4 x 3 x 9

B solve using the procedures that produce equivalent

This preview shows page 21 - 38 out of 77 pages.

b. Solve using the procedures that produce equivalent equations. – 9
Image of page 21
.
Image of page 22
. cont’d SOLUTION
Image of page 23
Classify each equation as a contradiction, a conditional equation, or an identity. 5
Image of page 24
ABSOLUTE VALUE EQUATIONS
Image of page 25
DEFINITION The absolute value of a number a is given by ABSOLUTE VALUE EQUATIONS . line number real the on a and x between ce tan dis the is a x , generally More . origin the to a of ce tan dis the represents it that and 0 a if a 0 a if a a
Image of page 26
ABSOLUTE VALUE EQUATIONS
Image of page 27
The following property is used to solve absolute value equations. A Property of Absolute Value Equations For any variable expression E and any nonnegative real number k , | E | = k if and only if E = k or E = – k ABSOLUTE VALUE EQUATIONS
Image of page 28
EXAMPLE If | x | = 5, then x = 5 or x = –5. If | x | = , then x = or x = – . If | x | = 0, then x = 0. ABSOLUTE VALUE EQUATIONS
Image of page 29
SOLVE AN ABSOLUTE VALUE EQUATION Solve: | 2 x – 5 | = 21 Solution: | 2 x – 5 | = 21 implies 2 x – 5 = 21 or 2 x – 5 = –21. Solving each of these linear equations produces 2 x – 5 = 21 or 2 x – 5 = –21 2 x = 26 2 x = –16 x = 13 x = –8
Image of page 30
SOLVE EACH EQUATIONS 14 5 7 3 . 2 3 5 2 . 1 x x 2 3 1 - x . 4 15 6 5 3 . 3 x x
Image of page 31
FORMULAS
Image of page 32
Image of page 33
Table 1.2 Formulas from Geometry FORMULAS
Image of page 34
It is often necessary to solve a formula for a specified variable. Begin the process by isolating all terms that contain the specified variable on one side of the equation and all terms that do not contain the specified variable on the other side. FORMULAS
Image of page 35
a . Solve 2 l + 2 w = P for l . b. Solve S = 2( wh + lw + hl ) for h . Solution: P w SOLVE A FORMULA FOR A SPECIFIED VARIABLE EXAMPLE
Image of page 36
b . S = 2( wh + lw + hl ) S = 2 wh + 2 lw + 2 hl S – 2 lw = 2 wh + 2 hl S – 2 lw = 2 h ( w + l) cont’d
Image of page 37
Image of page 38

You've reached the end of your free preview.

Want to read all 77 pages?

  • Spring '12
  • edgar
  • Math, Equations, Elementary algebra, ESTRADA, Division Property of Equality

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture