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Single-Variable Expressions Study Guide (page 2)

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Updated on Oct 3, 2011

Evaluating Single-Variable Expressions

Now that we know how to handle many operations in an expression, we can look at how to evaluate algebraic expressions. The most basic algebraic expressions contain only one variable, and these are called single-variable expressions. When we are given a value for the variable, we can replace that variable with the value (in parentheses).

Example

What is 6x when x = 4?

Replace x in the expression 6x with 4: 6(4) = 24. When x = 4, 6x = 24. But what if x = –10? Then we would replace x with –10: 6(–10) = –60. The value of 6x varies depending on the value of x. This is why x is called a variable!

Example

What is –5p + 9 when p = –1?

Replace p with –1: –5(–1) + 9. Remember the order of operations: Multiply before adding. –5(–1) = 5, 5 + 9 = 14. When p = –1, –5p + 9 is equal to 14.

Example

What is 4(c2 – 7) when c = –3?

Replace c with –3: 4((–3)2 – 7). (–3)2 – 7 is in parentheses, and since exponents come before subtraction, begin there. (–3)2 = 9, 9 – 7 = 2. Finally, 4(2) = 8.

Simplifying Expressions

Some expressions may have only one variable, but that variable appears more than once in the expression. For instance, 8x + 2x, or 2(j – 6) – 7j. We have two choices for evaluating these expressions. We can replace every occurrence, or instance, of the variable with its value, or we can simplify the expression first and then replace the variable with its value.

Example

What is 5v – 8v when v = 10?

First, try replacing every v with 10: 5(10) – 8(10).

Multiplication comes before subtraction, so multiply first: 5(10) = 50 and 8(10) = 80.

The expression is now 50 – 80.

Subtract: 50 – 80 = –30.

Now, evaluate the expression again, only this time, simplify it first Remember, to subtract like terms, subtract the coefficient of the second term from the coefficient of the first term, and keep the exponent and base: 5v – 8v = –3v.

Replace v with 10 and multiply: –3(10) = –30.

Either way, we arrive at the same answer. Which way was easier? That is up to you. You might find simplifying first easier, or you might prefer to just substitute the variables with their values right away. As long as you follow the order of operations, both methods will work.

Tip:

Some expressions cannot be simplified, or can be only partially simplified, often because they do not contain like terms. To evaluate 3x + 3x2 when x= 1, replace both x's with 1 because 3x and 3x2 cannot be combined.

Find practice problems and solutions for these concepts at Single-Variable Expressions Practice Questions.

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