1.4 Solving Absolute-Value Equations

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Presentation transcript:

1.4 Solving Absolute-Value Equations Objective 1 Solve absolute-value equations. Essential Question: How many solutions does an absolute value equation have ? VOCABULARY An absolute-value equation is an equation of the form |ax + b| = c.

The equation has two solutions: 7 and –3. Solving an Absolute-Value Equation Solve | x  2 |  5 The expression x  2 can be equal to 5 or 5. You must write two equations, one using 5 and the other –5 X – 2 = 5 X – 2 = –5 +2 +2 +2 +2 X = 7 X = –3 The equation has two solutions: 7 and –3. CHECK | 7  2 |  | 5 |  5 | 3  2 |  | 5 |  5

X = 6 and -5 Solve | 4x – 2 | = 22 4x – 2 = 22 4x – 2 = –22 +2 +2 +2 +2 +2 +2 4x = 24 4x = –20 4 4 4 4 x = 6 x = – 5 X = 6 and -5

+ 5 +5 | 2x – 7 | = 9 2x – 7 = 9 2x – 7 = – 9 +7 +7 +7 +7 2x = 16 Solve | 2x  7 |  5  4 + 5 +5 | 2x – 7 | = 9 First add 5 to both sides Write two equations one with 9 and the other with – 9 2x – 7 = 9 2x – 7 = – 9 +7 +7 +7 +7 2x = 16 2x = –2 2 2 2 2 X = 8 X = – 1 x  8 x  1 TWO SOLUTIONS x  8 x  1

|x + 3| = -5 NO SOLUTIONS Left Column Question Why are there no numbers that are solutions? |x – 12| = 0 12 Only Left Column ? Why is there only one solution?