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Statistics Geometry Programming Management. Economics Biology Trigonometry Calculus. On a number line , a negative version of a number is the same distance from zero as the positive, but in the opposite direction. Adding two negative numbers together makes the number more negative in other words, the digits will be higher, but since the number is negative, it counts as being lower Two negative signs cancel out — subtracting a negative number is the same as adding a positive number Multiplying or dividing two negative numbers gives a positive answer.
Multiplying or dividing a positive number and a negative number gives a negative answer. Know how to keep long problems organized. While simple algebra problems can be a snap to solve, more complicated problems can take many, many steps.
To avoid errors, keep your work organized by starting a new line every time you make a step toward solving your problem. These are called variables. Below are just a few common examples of variables in algebra: Think of variables as "unknown" numbers.
As mentioned above, variables are basically just numbers with unknown values. An easy way to start understanding variables is to replace them with question marks in algebra problems. The answer is again 4 , of course. Watch for recurring variables. If a variable appears more than once, simplify the variables. What do you do if the same variable appears more than once in the equation? Note again that you can only add the same variables together. This is also true for when one variable has a different exponent than another.
See How to Add Exponents for more information. Try to get the variable by itself in algebra equations. Solving an equation in algebra usually means finding out what the variable is. To figure out what the variable is, you need to get it by itself on one side of the equals sign. Whatever is left on the other side of the equals sign is your answer. However, to keep both sides of the equation equal, we also need to subtract 2 from the other side.
Cancel addition with subtraction and vice versa. As we just saw above, getting x by itself on one side of the equals sign usually means getting rid of the numbers next to it. To do this, we perform the "opposite" operation on both sides of the equation. In general, addition and subtraction are like "opposites" — do one to get rid of the other. Cancel multiplication with division and vice versa. Multiplication and division are a little harder to work with than addition and subtraction, but they have the same "opposite" relationship.
Cancel exponents by taking the root and vice versa. The "opposite" of an exponent is the root that has the same number as it.
It may be a little confusing, but, in these cases, you take the root of both sides when dealing with an exponent. For exponents, take the root. Use pictures to make problems clearer. You can even try using a group of physical objects like blocks or coins instead if you have some handy. Use "common sense checks" especially for word problems. When converting a word problem into algebra, try to check your formula by plugging in simple values for your variable. We can test whether this equation makes sense by plugging in simple values for w.
They can often be decimals, fractions, or irrational numbers. A calculator can help you find these complicated answers, but keep in mind that your teacher may require you to give your answer in its exact form, not in an unwieldy decimal. In this case, we may want to represent our answer as simply 7 or else simplify the answer by writing it in scientific notation. Try expanding your skill. One of the trickiest algebra skills of all is factoring — a sort of shortcut for getting complex equations into simple forms.
Below are just a few quick tips for factoring equations: Progress in algebra and any other kind of math requires lots of hard work and repetition. Ask your teacher to help you understand tricky algebra topics. Your teacher is the first person you should turn to with questions. After class, politely ask your teacher for help.
Many schools will have some sort of after-school program that can help you get the extra time and attention you need to start excelling at your algebra. Usually, in beginning algebra, graphing problems are restricted to equations with two variables usually x and y and are done on a simple 2-D graph with an x axis and a y axis. With these equations, all you need to do is plug in a value for x, then solve for y or do the reverse to get two numbers that correspond to a point on the graph.
Learn to solve inequalities. This means that every number less than one works for x. In other words, x can be 0, -1, -2, and so on. One algebra topic that many beginners struggle with is solving quadratic equations. Experiment with systems of equations. Often, algebra teachers use a graphing approach for solving these problems.
If we draw these two lines on a graph, we get one line that goes up at a steep angle, and one that goes down at a mild angle. Since these lines cross at the point -1,-5 , this is a solution to the system. Subtract 13 from both sides to get x by itself.
That makes the equation: Not Helpful 13 Helpful No, because the first equation asks for addition and the second equation asks for multiplication. Not Helpful 16 Helpful Algebra is a good tool for solving mathematical puzzles and situations that may arise in real life. Think about how you could apply it to your daily life. Not Helpful 19 Helpful Multiply b-1 by 7. Then subtract 8-b , which means you subtract 8 and add b. Not Helpful 12 Helpful Isolate the variable on one side of the equation and the constant on the other side.
In this example, subtract 3x from both sides, leaving no x on the left side and 3x on the right side. Then add 7 to both sides, leaving no constant on the right side and 11 on the left side.
Then divide both sides by the remaining coefficient of the variable. Not Helpful 14 Helpful Is x the exponent or the base? If it is the base, you will most likely have to factor it or use the quadratic equation. If the x is cubed, there are formulas you can memorize. If it raised to the fourth power, it often cannot be done by hand, unless by factoring.
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