Terms can be combined either by
adding or subtracting variables of the
same kind. One can also use multiplica-
tion and division to simplify an equation
by multiplying or dividing each side by
the same number (except 0). The follow-
ing are some examples:
- Adding like terms 4x 3 x14,
simplifies to 7x14. - The equation 4 8 x 10 4 x
2 20 can be simplified by com-
bining the like terms, which gives
the simplified result 12 4 x20. - If necessary, do a combination of
addition, subtraction, multiplica-
tion, or division. For example, the
equation 2x 2 4 x3, simpli-
fies to 2x 4 x5 (by adding 2 to
both sides); then subtract 2xfrom
both sides, simplifying to 0 2 x
5. (Note: Since subtracting any
number is the same as adding its negative, it is often more helpful to replace
subtractions with additions of a negative number.) Finally, subtract 5 from both
sides (or 2x5), divide both sides by 2, and the result is x5/2 (or 2.5). - To simplify expressions raised to a power, certain rules should be followed. For
example, for (x3)^2 4 x, square x3, or (x3)(x3), first squaring the
first term (xsquared equals x^2 ), then the second (3 squared equals 9), then mul-
tiply and add the inner and outer terms together (3x 3 x 6 x). By combining
like terms, the entire equation results in the simplified expression x^2 6 x 9
4 x, which finally equals x^2 2 x9.
What are some examplesof algebraic equation solutions?
The following lists some simple solutions to selected algebraic equations:
- To solve for the equation 4x 4 12
add 4 to each side: 4x 16
then divide both sides by 4: x16/4
then solve for x: x 4 - To solve for the equation (x3)^2 4 x(x1)^2 3
expand each side by first doing the operations within the parentheses: x^2 2 x
9 x^2 2 x (^4137)
ALGEBRA
René Descartes, who is more often remembered for
developing the concept of Cartestian coordinates,
also originated the idea of using letters when writing
equations that include unknown values. Library of
Congress.