How to Solve Intermediate Algebra Equations
If you have ever gotten stuck solving an intermediate algebraic equation, you're not alone. Students commonly experience frustration as they progress in algebra and face more challenging problems. While basic equations often require only one or two steps, solving an intermediate algebraic equation involves a more complicated thinking process. However, with patience, you can learn to use these steps to solve equations that don't involve rational expressions (fractions with variables) or logarithms.
Other People Are Reading
Instructions
-
-
1
Check to see whether the equation is a polynomial, a quadratic equation (a special type of polynomial), or neither. If the equation has a variable to more than one power, such as 3X^3 + X^2 - 5X = 8, than the equation is a polynomial and it must be solved using factoring or synthetic division. If the highest power involved is X^2, than you have a quadratic equation. To solve a quadratic equation, set the equation equal to zero (in this case, subtract 8 from both sides) and factor or use the quadratic equation. If it does not contain a variable to more than one power, continue following these steps.
-
2
Intermediate algebra equations often include multiple terms, or parts, on each side of the equation. If this is the case, you must first combine like terms on both sides. For instance, add any Xs to each other, any Xs squared to each other, and any plain numbers (called constants) to each other. For instance, the problem 2X + 5 + 6X - 7 = 5X +8X -3 would turn into 8X - 2 = 13X -3.
-
-
3
Next, take care of any parentheses or operations right outside of parentheses. For instance, if the equation looks like this: 6X - 7 = 2(4X-11), you must divide both sides by 2. Don't waste your time by distributing the number in front of the parentheses. Remember that a big division bar means there are invisible parentheses on both the top and bottom of it, and that a radical (square) root sign also acts like parentheses.
-
4
Look and see if there are variables (letters) on both sides of the equation. If there are, you must eliminate them from one side, preferably the right-hand side. Do this by performing the opposite operation of the one in the problem to both sides. For example, if 4X is being added to the right side in the equation, subtract 4X from both sides. Or, if the right-hand side is being divided by 8X, then multiply both sides by eight X. Addition and subtraction are opposites as are multiplication and division.
-
5
Next, take care of any coefficients in front of variables with exponents, or other special functions, that you did not eliminate in step 2. Do so by performing the opposite operation on both sides. For example, if you have 3X^3 = 24, divide both sides by 3.
-
6
At this point, you should have a simple equation with one term on each side. Get rid of any special functions such as exponents or square roots by doing the opposite to both sides. For example, for the equation X^2 = 16, you would take the square root of both sides and get +4 and -4 as your two answers.
-
7
Finally, eliminate any coefficients directly in front of the variable. For example, you would divide both sides of 3X =9 by three.
-
1
Tips & Warnings
Remember that a big division bar means there are invisible parentheses on both the top and bottom of it, and that a radical (square) root sign also acts like parentheses.
