If your argument is just a variable by itself, set equal to a number, then simplifying is very easy. Since absolute value represents a distance from 0, your variable could be either the positive number to which it is equal, or it could be the negative version of that number. There is no way to tell, so include both possibilities in your solution. For example, say you know that the absolute value of a variable, x, is equal to 3. You cannot tell if x is positive or negative; you are looking for any number whose distance is 3 from 0. Therefore, you solution is either 3 or -3. If this is the kind of argument you need to simplify, stop here. Your work is done. If, however, you have an inequality, continue on. If, however, you are given an argument with a variable, expressed as an inequality, more steps are required. Interpret these inequalities as asking you to find all the possible numbers that could work. For example, say you have the following inequality. This can be interpreted as "Show all numbers whose absolute value is less than 7." In other words, find all numbers whose distance is 7 from 0, excluding 7 itself. Note that the inequality is constructed as "less than" rather than "less than or equal to." If it were the later, then 7 itself would be included. The first thing to do, when faced with an absolute value inequality, is to draw a number line. Tag points corresponding with the numbers with which you are working. In the example above, your number line would look like this. The open circles indicate numbers excluded from your final result. Remember: if the inequality were stated as "greater than or equal to" or "less than or equal to," then these numbers would be included instead. In that case, the circles would be solid. Since you don't know whether your variable is positive or negative, you are really dealing with two possible ranges of numbers: those on the left side of the number line and those on the right. First, consider the numbers on the left. Make the variable negative, and convert your absolute value bars to parentheses. Solve. In the example above, you would convert the absolute value bars to parentheses to show that (-x) is less than 7. Multiply both sides of the inequality by -1. Note that when you multiply by a negative number, you must switch the inequality sign (from less than to greater than, or vice versa). Your inequality would look like this. You now know that for the left side of the number line, x will be greater than -7. On a number line, that would look like this. Now you can look at the other range of numbers, those that are positive. This is even simpler: make the variable positive, convert your absolute value bars to parentheses. In the example above, you would convert the absolute value bars to parentheses to show that (x) is less than 7. No further work is necessary for this step. On a number line, that would look like this. Once you have considered both sides, you need to determine where the solutions overlap. Draw both intervals on the same number line to get a final result. In the example above, you would highlight values greater than -7 and less than 7 (but excluding -7 and 7 themselves). These are your solutions.
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One-sentence summary -- Deal with an argument that is just a variable. Recognize absolute value inequalities. Graph a number line. Consider the numbers on the left side of the number line. Consider the numbers on the right side of the number line. Find the intersect of the two intervals.

Begin by melting 1 tbsp (15 grams) of butter in a small saucepan. You will know the butter is heated when you can sprinkle a pinch of flour over it and the mixture slowly starts to bubble. You can substitute oil for the butter to make it a dairy-free option. Keep the mixture over medium heat. Whisk it constantly while the flour begins to bubble. As the flour and butter cook, they will become smooth and start to thin. Roux does not take long to prepare. It is done when the flour loses its raw smell, and it becomes a thin, white paste. Use roux to thicken milk-based sauces, such as cheese sauce for macaroni and cheese. You can let the roux cook longer to get a blond, brown, or dark brown roux, but these are commonly used to thicken soups and chowders, not sauces. Whisk the mixture vigorously. Cool your hot roux in the fridge or let it sit out on the counter until it reaches room temperature. Hot roux can be added to cold or warm sauces right away. Do not add hot roux to a hot liquid, as it will create lumps that can not be removed unless you use a strainer. Turn the stove heat up to high and allow your sauce to come to a boil. The mixture will only take about 1 minute to begin thickening. Keep your sauce at a boil until it has reached your desired thickness. Place your roux in the refrigerator to let it cool overnight or until it has hardened. Keep any leftover roux in an airtight container and freeze it or refrigerate it for up to a month. Roux made with oil can be stored at room temperature for 2-4 weeks.
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One-sentence summary -- Melt the butter in a saucepan over medium heat. Whisk 1 tbsp (9 grams) of flour into the butter until a thick paste forms. Stir the mixture while you cook it for 5 minutes. Add room temperature roux to your hot liquid. Boil the sauce 1 minute on high. Pour any leftover roux onto a baking sheet or ice cube tray.

This first rectangle will be the frame of your house. The exact proportions of the rectangle don't matter, but try not to make it too long and thin or your house might not look realistic. Use a ruler or straightedge to draw the rectangle so all of the lines are neat and straight. The base of the triangle should line up with the top of the rectangle. Make the triangle wide enough that the bottom corners extend past the sides of the rectangle. The triangle should be around the same height as the rectangle. If you make it too tall it won't look realistic. To make the chimney, draw a tall, narrow rectangle that extends up off the left side of the roof. Then, draw a smaller, horizontal rectangle on top of it. To make the roof panels, draw evenly-spaced horizontal lines from one side of the roof to the other. The number of panels you draw doesn't matter, but try to keep the space between each panel the same.
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One-sentence summary --
Draw a rectangle. Sketch a triangle on top of the rectangle to make the roof. Add a chimney and some horizontal panels to the roof.