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Unformatted text preview: ill start off this chapter with a fairly short section with some basic terminology that we use
on a fairly regular basis in solving equations and inequalities.
First, a solution to an equation or inequality is any number that, when plugged into the
equation/inequality, will satisfy the equation/inequality. So, just what do we mean by satisfy?
Let’s work an example or two to illustrate this. Example 1 Show that each of the following numbers are solutions to the given equation or
(a) x = 3 in x 2 - 9 = 0 [Solution]
(b) y = 8 in 3 ( y + 1) = 4 y - 5 [Solution]
(c) z = 1 in 2 ( z - 5 ) £ 4 z [Solution]
(d) z = -5 in 2 ( z - 5 ) £ 4 z [Solution]
(a) We first plug the proposed solution into the equation.
? 32 - 9 = 0
9-9 = 0
0=0 OK So, what we are asking here is does the right side equal the left side after we plug in the proposed
solution. That is the meaning of the “?” above the equal sign in the first line.
Since the right side and the left side are the same we say that x = 3 satis...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12