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Like any puzzle, there are pieces. Learning how to recognize the numbers and symbols for the placeholders that they are makes the solution much easier to grasp. Try to find the missing number in a problem where the final answer is given. For example: 1+x=9{\displaystyle 1+x=9}. The missing number is 8, because 1 plus 8 equals 9. Pretty simple, right? This is basic algebra. When solving an algebraic problem, you must remember that if you alter one side of the equation in any way, you must do the exact same thing to the other side of the equation. If you add, subtract, multiply, or divide, you must perform the same operation to the opposite side. For example, to solve x+3=2x−1{\displaystyle x+3=2x-1}, you first need to subtract x{\displaystyle x} from both sides of the equation, then add 1 to both sides of the equation:  x+3−x=2x−1−x{\displaystyle x+3-x=2x-1-x}3=x−1{\displaystyle 3=x-1}3+1=x−1+1{\displaystyle 3+1=x-1+1}4=x{\displaystyle 4=x} When given an algebraic expression, you will notice that there are constants and variables. A constant is any number given, while a variable is a letter that represents an unknown number.  To isolate the variable, add or subtract terms to get the variable on one side. If the variable has a coefficient, divide both sides by that coefficient to get the variable alone. For example, to solve 6y+6=48{\displaystyle 6y+6=48}, you first need to subtract 6 from both sides, then divide by 6:  6y+6−6=48−6{\displaystyle 6y+6-6=48-6}6y=42{\displaystyle 6y=42}6y6=426{\displaystyle {\frac {6y}{6}}={\frac {42}{6}}}y=7{\displaystyle y=7} If you are solving for a variable that is squared, you will need to take the square root of it to solve the problem. Conversely, If the variable is a square root, then you will need to square it to solve the problem. Remember that whatever you do to one side of the equation, you must do to the other side.  For example, to solve x=9{\displaystyle {\sqrt {x}}=9}, you need to square both sides of the equation:  (x)2=92{\displaystyle ({\sqrt {x}})^{2}=9^{2}}x=81{\displaystyle x=81}   To solve x2=16{\displaystyle x^{2}=16}, you need to take the square root of both sides of the equation:  x2=16{\displaystyle {\sqrt {x^{2}}}={\sqrt {16}}}x=4{\displaystyle x=4} Whenever you have terms that have the same variable, you can combine them to simplify the problem. This helps to keep equations manageable and easier to solve. Remember, terms that have different exponents are not identical terms: x{\displaystyle x} is not the same as x2{\displaystyle x^{2}}.  The following are like terms: 4x,−3x,0.45x,−132x{\displaystyle 4x,-3x,0.45x,-132x}  The following are not like terms: 5x,8y2,−13y,9z,12xy{\displaystyle 5x,8y^{2},-13y,9z,12xy}  For example: 4x+3y−7x{\displaystyle 4x+3y-7x} has two like terms, 4x{\displaystyle 4x} and −7x{\displaystyle -7x}. To combine them, add:  (−7x+4x)+3y{\displaystyle (-7x+4x)+3y} = −3x+3y{\displaystyle -3x+3y} The art of mastering any concept is practice. Try solving problems with increasing difficulty to truly check your comprehension. Use problems from your textbook or seek out extra problems online. For example, solve q+18=9q−6{\displaystyle q+18=9q-6}  Add 6 to both sides: q+18+6=9q−6+6{\displaystyle q+18+6=9q-6+6}q+24=9q{\displaystyle q+24=9q}  Subtract q{\displaystyle q} from both sides: q+24−q=9q−q{\displaystyle q+24-q=9q-q}24=8q{\displaystyle 24=8q}  Divide both sides by 8: 248=8q8{\displaystyle {\frac {24}{8}}={\frac {8q}{8}}}3=q{\displaystyle 3=q} Make a habit of checking your answers when you have solved a problem. Once you have obtained the solution and discovered the value of the variable, check your work by inserting the number you have obtained into the original equation. If the expression is still true, then you have found the correct solution! For example, if you found that q=3{\displaystyle q=3}, to check your answer, substitute 3 for q{\displaystyle q} in the original equation: q+18=9q−6{\displaystyle q+18=9q-6}.   3+18=9(3)−6{\displaystyle 3+18=9(3)-6}21=27−6{\displaystyle 21=27-6}21=21{\displaystyle 21=21}  Right! Since the equation is true, you know that your solution is correct.
Recognize that algebra is just like solving a puzzle. Perform operations on both sides of the equation. Isolate the variable on one side of the equation. Take the root of the number to cancel an exponent. Combine like terms. Practice with more complex problems. Check your answers.