UNIT 4, LESSON 5 Absolute Value Equations. Review of Absolute Value ions/absolutevalue/preview.weml

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Presentation transcript:

UNIT 4, LESSON 5 Absolute Value Equations

Review of Absolute Value ions/absolutevalue/preview.weml ions/absolutevalue/preview.weml

The absolute-value of a number is that numbers distance from zero on a number line. For example, |–5| = 5. 55 44 33 2 66 11 6 5 units Both 5 and –5 are a distance of 5 units from 0, so both 5 and –5 have an absolute value of 5.

1.Isolate the absolute-value expression 2.Split the problem into two cases. How to Solve Absolute Value Equations:

Solve the equation. |x| – 3 = |x| = 7 x = 7 –x = 7 –1(–x) = –1(7) x = –7

Solve |a| – 3 = |a| = 8 a = 8 or a = –8 Example:

Solve the equation. |x  2| = 8 +2 x  2 = 8 x = x =  6 x  2 =  8

Solve |3c – 6| = 9 3c – 6 = 9 3c – 6 = – c = c = 5 Example: + 6 3c = –3 3 3 c = –1

|x + 7| = 8 x + 7 = 8 x + 7 = –8 – 7 –7– 7 x = 1 x = –15 3 3

Not all absolute-value equations have solutions. If an equation states that an absolute-value is negative, there are no solutions. CAREFUL!

Solve the equation. 2  |2x  5| = 7  2  |2x  5| = 5 Absolute values cannot be negative. |2x  5| =  5 This equation has no solution.  1