Summarize:

When you have one or more algebra problems, you must read the instructions carefully. Look for key words in the instructions like "solve," "simplify," "factor," or "reduce." These are some of the most common instructions (although there are others that you will learn). Many people have problems because they try to "solve" a problem when they really only need to "simplify" it. When you read the problem instructions, you should identify the key words and then perform those operations. Many people feel frustration with algebra when they try doing something that is not really part of the intended problem. The basic operations you will be asked for are: Solve. You will need to reduce the problem to an actual numerical solution, such as "x=4." You need to find a value for the variable that can make the problem come true. Simplify. You need to manipulate the problem into some simpler form than before, but you will not wind up with what you might consider "an answer." You will probably not have a single numerical value for the variable. Factor. This is similar to "simplify," and is usually used with complex polynomials or fractions. You need to find a way to turn the problem into smaller terms. Just as the number 12 can be broken into factors of 3x4, for example, you can factor an algebraic polynomial. For example, a simple expression like 5x{\displaystyle 5x} can be broken into factors of 5{\displaystyle 5} and x{\displaystyle x}. For example, the expression x2+3x+2{\displaystyle x^{2}+3x+2} can be factored into the terms (x+2){\displaystyle (x+2)} and (x+1){\displaystyle (x+1)}. Reduce. To "reduce" a problem generally involves a combination of factoring and then simplifying. You would break the terms of a numerator and denominator into their factors. Then look for common factors on top and bottom, and cancel them out. Whatever remains is the "reduced" form of the original problem. For example, reduce the expression 6x22x{\displaystyle {
rac {6x^{2}}{2x}}} as follows: 1. Factor the numerator and denominator: (3)(2)(x)(x)(2)(x){\displaystyle {
rac {(3)(2)(x)(x)}{(2)(x)}}} 2. Look for common terms. Both the numerator and denominator have factors of 2 and x. 3. Eliminate the common terms: (3)(2)(x)(x)(2)(x){\displaystyle {
rac {(3)(2)(x)(x)}{(2)(x)}}} 4. Copy down what remains: 3x{\displaystyle 3x} " In algebra, the difference between an "expression" and an "equation" is very important. An expression is any group of numbers and variables, collected together. Some examples of expressions are x{\displaystyle x}, 14xyz{\displaystyle 14xyz} and 2x+15{\displaystyle {\sqrt {2x+15}}}. All you can do to an expression is simplify or factor it. An equation, on the other hand, contains an = sign. You can simplify or factor equations, but you can also solve them to get a final answer. It is important to look for the difference. If you have an expression, like 4x2{\displaystyle 4x^{2}}, you can never find a single "answer" or "solution." You could find out that if x=1{\displaystyle x=1}, then the expression would have a value of 4, and if x=2{\displaystyle x=2}, then the expression would have a value of (4)(2)2{\displaystyle (4)(2)^{2}}, which is 16. But you cannot get a single "answer."
Read the problem instructions carefully. Perform the operations that are instructed. Learn the difference between "expression" and "equation.