Write an article based on this "Write the equation in standard form. Reduce the equation if possible. Check for the impossibility of a solution."
article: A linear equation is one that has no exponents greater than 1 on any variables. To solve a linear equation in this style, you need to begin by writing it in what is called "standard form." The standard form of a linear equation looks like Ax+By=C{\displaystyle Ax+By=C}, where A,B{\displaystyle A,B} and C{\displaystyle C} are integers. If the equation is not already in standard form, you need to use the basic rules of algebra to rearrange or combine the terms to create the standard form. For example, if you begin with 23x+4y7x=3y+15{\displaystyle 23x+4y-7x=-3y+15}, you can combine similar terms to reduce the equation to 16x+7y=15{\displaystyle 16x+7y=15}. When the equation is in standard form, check all three terms A,B{\displaystyle A,B} and C{\displaystyle C}. If there is a common factor in all three terms, then reduce the equation by dividing all terms by that factor. If you reduce evenly across all three terms, then any solution you find for the reduced equation will also be a solution for the original equation. For example, if all three terms are even, you can at least divide by 2, as follows: 42x+36y=48{\displaystyle 42x+36y=48} (all terms are divisible by 2) 21x+18y=24{\displaystyle 21x+18y=24} (all terms now are divisible by 3) 7x+6y=8{\displaystyle 7x+6y=8} (this equation is as reduced as possible) In some cases, you may be able to tell immediately if there is no solution to your problem. If you see a common factor on the left side of the equation that is not shared on the right side, then there can be no solution to the problem. For example, if both A{\displaystyle A} and B{\displaystyle B} are even, then the sum of the left side of the equation would have to be even. But if C{\displaystyle C} is odd, then there will be no integer solution to the problem. 2x+4y=21{\displaystyle 2x+4y=21} will have no integer solution. 5x+10y=17{\displaystyle 5x+10y=17} can have no integer solution, because the left side of the equation is divisible by 5, but the right side is not.

Write an article based on this "Write down the basic formula for finding the perimeter of a rectangle. Find the length and the width of your rectangle. Add the length and width. Multiply the sum of the length and width by two. Add l + l + w + w."
article: This formula will help guide you as you calculate the perimeter of your own rectangle. The basic formula is: P = 2 * (l + w). Perimeter is always the total distance around the outside edge of any shape, whether it is simple or compound. In this equation, P stands for "perimeter," l refers to the length of the rectangle, and w refers to the width of the rectangle. Length always has a greater value than width. Because opposite sides of a rectangle are equal, both lengths will be the same and both widths will be the same. This is why you write the equation as a multiplication of the sum of the length and width by 2. You can also write the equation as P = l + l + w + w to make this very clear. For a basic math problem at school, the length and width of the rectangle will be provided in the problem. These are usually next to the figure of the rectangle. If you are calculating the perimeter of a rectangle in real life, use a ruler, yardstick, or tape measure to find the length and width of the area that you are trying to measure. If you're measuring outdoors, measure all sides to see if the opposites are truly congruent. For example, l = 14 centimeter (5.5in), w = 8 centimeter (3.1in). After you identify your length and width, you want to plug them into the "l" and "w" slots in the perimeter equation. When you are working out your perimeter equations, note that according to the order of operations, mathematical expressions contained inside brackets or parentheses are solved before those outside of the parentheses. So, you'll begin solving your equation by adding the length and width. For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22). When you're looking the formula for the perimeter of a rectangle, the "(l + w)" is multiplied by two. Once you've completed this multiplication, you have the perimeter of your rectangle. This multiplication takes into account the other two sides of your rectangle. When you added together the width and length, you only added together two sides of the shape. Since the other two sides of the rectangle are equal to the two already added together, you can simply multiply this measurement by two in order to find the total sum of all four sides. For example, P = 2 * (l + w) = 2 * (14 + 8) = 2 * (22) = 44 centimeter (17.3in). Instead of adding two sides of your rectangle and multiplying by two, you can simply add all four sides together directly to find the perimeter of your rectangle. If you struggle with the concept of perimeter, this is a great place to start. For example, P = l + l + w + w = 14 + 14 + 8 + 8 = 44 centimeter (17.3in).

Write an article based on this "State your interest simply if you are still just friends. Share your concerns with your best friend to maintain honesty. Establish the boundaries of your new relationship to avoid misunderstandings. Avoid making assumptions about what your partner wants."
article:
If your friend doesn't know that you have a romantic interest in them, tell them in a straightforward but non-threatening way. Explain that you are attracted to them and want to pursue a romantic relationship with them. Make it clear that you will understand if they don't feel the same way but that you wanted to be honest about your feelings either way. For instance, say, "I have strong feelings for you and I want to be more than just a friend, but I will totally understand if you aren't interested in taking things to the next level." An unrequited crush can put tension on a friendship over time, so it is good to be honest regardless of the outcome. Moving from friendship to romance is a risk that may be challenging to take. Share any worries you have about losing your close relationship to see if they feel the same way. Ask if there are any other concerns about the situation that they have to get a clear understanding of what obstacles may be facing you both. For example, say something like, "You're my best friend and I'm not sure if my romantic feelings for you are worth losing you entirely." Communicate your romantic wants and needs clearly to your partner from the start. Avoid the assumption that they will intuitively know how what will be okay with you and make you happy. Be sure to outline any behaviour that you consider unacceptable from a romantic partner so they know how you want to be treated. For instance, say something like, "I believe in monogamy and I can't tolerate cheating in a romantic relationship." After transitioning from friendship to a relationship, you may think that you already know what your partner wants romantically. Always check with your partner to see what goals and desires they have as these may change over time, and in different situations. If you catch yourself guessing what they might like, stop and ask them about it to double check. They will appreciate your effort and concern about their feelings. For instance, if your partner noted in the past that they didn't want a co-dependent relationship, do not assume that they want you to keep your distance.