+2446 Doing this problem requires one to consider a few cases.
Firstly, I will solve for x in the first given equation.
| \(|x-y|=950\) | Drop the absolute value bars and split this equation into a positive and negative answer. | ||
| Add y to both sides in both cases to isolate x. | ||
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Now, let's solve for z in the second equation in the exact same fashion.
| \(|y-z|=987\) | Drop the absolute value bars again. | ||
| Subtract y from both sides. | ||
| Divide by -1 to fully isolate. | ||
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In order to solve this problem, one must consider all 4 cases. I have created them all in a table for you! Then, simplify as much as possible.
| Case 1: \(|x_1-z_1|\) | Case 2: \(|x_1-z_2|\) | Case 3: \(|x_2-z_1|\) | Case 4: \(|x_2-z_2|\) |
| \(|y+950-(y-987)|\) | \(|y+950-(y+987)|\) | \(|y-950-(y-987)|\) | \(|y-950-(y+987)|\) |
| \(|y+950-y+987|\) | \(|y+950-y-987|\) | \(|y-950-y+987|\) | \(|y-950-y-987|\) |
| \(|950+987|\) | \(|950-987|\) | \(|-950+987|\) | \(|-950-987|\) |
| \(|1937|\) | \(|-37|\) | \(|37|\) | \(|-1937|\) |
| \(1937\) | \(37\) | \(37\) | \(1937\) |
Therefore, \(|x-z|=37\hspace{1mm}\text{or}\hspace{1mm}|x-z|=1937\)
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<---- You
