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Building onto the proposed solution offered by Bunuel, what helped me was to draw out the graphs and use graph transformation to determine the desired area specified by the question.
The line equation to start off can be y = -x+5. From the graph, there is only 1 portion where y takes positive values for POSITIVE x values.
Since the question indicates |x|, flip the curve about the y axis to obtain y = x + 5. In this case, find the portion where y takes positive values with NEGATIVE x values.
So x and |x| options have been explored now. Move on to |y| values.
Going back to the base equation y = -x+5, we can flip the graph about x axis to obtain y = x -5. This is done because ALL values of original y equation are reversed now! The desired region should be the area where y is NEGATIVE for positive x values.
Do this one more time to flip the graph y = x + 5 about the x axis. We will obtain y = -x - 5. The desired region will then be the area with NEGATIVE y values for NEGATIVE x values.
SO in the end, there are 4 small triangles that fulfil the condition set out in the question = 4 * 1/2 * 5 * 5 = 50.
The line equation to start off can be y = -x+5. From the graph, there is only 1 portion where y takes positive values for POSITIVE x values.
Since the question indicates |x|, flip the curve about the y axis to obtain y = x + 5. In this case, find the portion where y takes positive values with NEGATIVE x values.
So x and |x| options have been explored now. Move on to |y| values.
Going back to the base equation y = -x+5, we can flip the graph about x axis to obtain y = x -5. This is done because ALL values of original y equation are reversed now! The desired region should be the area where y is NEGATIVE for positive x values.
Do this one more time to flip the graph y = x + 5 about the x axis. We will obtain y = -x - 5. The desired region will then be the area with NEGATIVE y values for NEGATIVE x values.
SO in the end, there are 4 small triangles that fulfil the condition set out in the question = 4 * 1/2 * 5 * 5 = 50.
