Solving Absolute Value Equations On Both Sides
Camila Farah
We ll leave it to you to verify that the first potential solution does in fact work and so there is a single solution to this equation.
If we have absolute value signs on both sides of the equation we can play the same game with two choices as follows. But wait we can t have a negative number as a solution. Multiply both sides by x 6 x 6 6. The same method can be applied when there are absolute values on both side of the equation.
Perhaps the most common need for using absolute value is considering distance differences. Solve x 2 3 x. If you so wish you can substitute these values of color red x in both color green case 1 and color green case 2 to verify the accuracy. We can write 3x 4 2x 3 or 3x 4 2x 3.
Solving the second equation. Solve 3x 4 2x 3 solution. Can we use the same method. In case you want to see the examples on solving absolute value equations on both sides first go to the middle of the post for the examples and explanations.
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Color blue rarr x 4 3. 11 2 15 2 2. 11 4 3 4 2. Hence there are two solutions for the absolute value equation.
Let s consider the following equation. 3x 3 2x 5 3x 3 2x 5. Absolute values on both side of the equation. The exercises are in the next section.
Equations that have absolute value signs on both sides. Absolute value exercises. 5 2 3 3 5 2 2. Why use absolute values.
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X frac 1 4 and notice that this is less than 2 as our assumption required and so is a solution to the equation with the absolute value in it. 1 4 3 3 1 4 2.
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