Expressions are made of variables, or letters that take the place of unknown numbers. But what if we know the numbers? We can take out the variable, replace it with the number, and do the math. This is called evaluating an algebraic expression.
If we have the expression 3x + 1 and we find out that x = 10, we can evaluate it. The expression means "three times whatever x is, plus one."
We rewrite the expression, replacing the x with 10 in parentheses, and do the math.
3x + 1 =
3(10) + 1 =
30 + 1 =
31
Sample Problem
Evaluate 4xy + 3x if x = 8 and y = 5.
We take out all the variables and put in the numbers in parentheses. Replace x with 8 and swap out y with 5.
4xy + 3x =
4(8)(5) + 3(8) =
160 + 24 = 184
Don't Forget: we'll need our faithful friend PEMDAS (a.k.a. the Order of Operations) to make sure we do the math in the right order.
Example 1
Evaluate the following expression when x = 2, y = -3, and z = -1.
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Example 2
Find the values of the following expression for x = -2, -1, 0, 1, and 2.
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Example 3
Which of the following values make the equation x4 – 1 = 0 true? x = -2, -1, 0, 1, 2 |
Exercise 1
Evaluate the expression 3x2 + 5xy – 2 for x = 3 and y = -2.
Exercise 2
The formula for the surface area of a cone is πrs + πr2, where r is the radius of the base and s is the length of the slant. Find the surface area of a cone with radius 10 cm and a slant of 12 cm (use 3.14 for π).
Exercise 3
Evaluate the expression x3 + x2 + x + 1 for x-values equal to -2, -1, 0, 1, and 2.
Exercise 4
Which of the following values of x make the equation x2 – 8x = -12 true?
x = 1, 2, 3, 4, 5, 6