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Solving absolute value equations.?
Okay so here is the equation:
4 l x+2 l - 16 = 0
and it tells me to rewrite the equation in standard form and determine if there is a solution.
could someone please help me with this?
thanks :)
1 Answer
- InformationLv 68 years agoFavorite Answer
4|x + 2| - 16 = 0 => Write down equation.
4|x + 2| = 16 => Move 16 to the other side.
|x + 2| = 4 => Divide each side by 4.
Here we have two cases. When the answer is positive and when the answer is negative. Thus, you have two values and solutions for x.
x + 2 = 4 ==> x = 4 - 2 = 2
x + 2 = -4 ==> x = -4 - 2 = -6
Solutions: x = 2, x = -6;
~Maths
- Anonymous8 years ago
solving absolute value equations is equivalent to solving inequalities -- you divide the domain x into intervals, wherever the absolute value changes sign. then resolve the sign associated with the absolute value in each interval, and simplify the resulting expression.
in the given, the intervals to consider are (x > -2) and (x < -2)
in (x > -2) the expression is 4(x+2) - 16 = 0
in (x < -2) the expression becomes -4(x+2) - 16 = 0
now just solve for x and make sure it is in the interval -- if it is not, then a solution to the equation does not exist for that interval.
