4 x 3 3 x 3 x 4x 3 3 x or or 3 x

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Unformatted text preview: - 8 = -1 5y = 7 7 y= 5 In this case the two solutions are y = or or or 5y - 8 = 1 5y = 9 9 y= 5 7 9 and y = . 5 5 [Return to Problems] Now, let’s take a look at how to deal with equations for which b is zero or negative. We’ll do this with an example. Example 2 Solve each of the following. (a) 10 x - 3 = 0 (b) 5 x + 9 = -3 Solution (a) Let’s approach this one from a geometric standpoint. This is saying that the quantity in the absolute value bars has a distance of zero from the origin. There is only one number that has the property and that is zero itself. So, we must have, 10 x - 3 = 0 Þ x= 3 10 In this case we get a single solution. (b) Now, in this case let’s recall that we noted at the start of this section that p ³ 0 . In other words, we can’t get a negative value out of the absolute value. That is exactly what this equation is saying however. Since this isn’t possible that means there is no solution to this equation. So, summarizing we can see that if b is zero then we can just drop the absolute value bars and solve the equation. Likewise, if b is negative then there will be no solution to the equation. To this point we’ve only looked at equatio...
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