![]() the difference between 5 times a number and 2 times the same number One more than the product of 2 and a numberĦ. 3 multiplied by the number represented by xģ. two times the quantity found by adding a number to 1 ![]() The following examples illustrate how certain key words can be translated into algebraic symbols.ġ. So, if a problem is stated in English, we can translate the phrases into algebraic symbols and proceed to solve the problem according to the rules developed for algebra. We want to be able to change English phrases into their “algebraic” equivalents, and vice versa. Simplify the following expressions by combining like terms.Īlgebra is a language of mathematicians, and in order to understand mathematics, you must understand the language. Click on "Solve Similar" button to see more examples. Let’s see how our math solver solves this and similar problems. (x+3x)/2+x=(4x)/2+x A fraction bar is a symbol of inclusion like parentheses. Like terms can be combined by adding (or subtracting) the coefficients.Įxamples Combine like terms whenever possibleģ. We say that 3x and 5x have been combined or that we have combined like terms. ![]() This last form is particularly useful when b and c are numerical coefficients. Thus, in the term 8x,8 is the coefficient of x.Įxpressions with like terms can be simplified by applying the distributive property discussed in Section 1.1 to integers. ![]() The numerical part of a term is called the coefficient of the variable or variables in the term. Also, -2x and 5x are like terms, but -2x and 3x^2 are not like terms because x and x^2 are not the same power of x. Like terms (or similar terms) are those terms that are constants or contain variables that are of the same power in each term. The expressions 3+x,5y-7x,3x+4x, and 5x^2-3x^2+2x are the sums of terms. To evaluate an algebraic expression that involves the sums and/ or differences of several terms, substitute the chosen value for each variable throughout the expression, then apply the rules for order of operations.Įvaluate the following expressions if x=3 and y=-1Ħ. A single constant or variable is also a term. x^2=-3^2=-9 or -x^2=-1*x^2=-1*3^2=-1*9=-9Īn expression that involves only multiplications and/or divisions with constants and/or variables is called a term. Suppose x=3 and we want to evaluate the expression -x^2. Is there a difference between (-7)^2 and -7^2, or are they the same? In the expression (-7)^2, the base is -7 and -7 is to be squared:īut, for -7^2, the base is 7 and the rules for order of operations say to square 7 first: (2^5+4)/6-4(-2)(The fraction bar should be treated as a symbol of inclusion.) From left to right, perform additions and subtractions as they appear. From left to right, perform multiplications and divisions as they appear.Ĥ. Work within symbols of inclusion (parentheses, brackets, or braces),beginning with the innermost pair.ģ. The same set of rules for order of operations for whole numbers discussed in
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