When given an algebraic expression, one of the most common things to do with it is evaluate it for some given value of the variable.
Take a look at this example to see how this works:
Let x = 12. Find the value of 2x - 7.
To find the solution, substitute 12 in place of x in the given expression.
Note: In the first step of the problem, keep the substituted value in parentheses. This makes the written-out problem easier to follow, and helps avoid mistakes. (If we didn’t use parentheses and also forgot to add a multiplication sign, we would end up turning "2x" into "212" instead of "2 times 12!")
Evaluating an Expression
Let y=−2. Find the value of 7y−11y+2.
Many expressions have more than one variable in them. For example, the formula for the perimeter of a rectangle, P=2l+2w, has two variables: length (l) and width (w). Be careful to substitute the appropriate value in the appropriate place.
Evaluating an Expression with Multiple Variables
The area of a trapezoid is given by the equation A=h2(a+b). Find the area of a trapezoid with bases a=10 cm and b=15 cm and height h=8 cm.
To find the solution to this problem, substitute the given values for variables a, b, and h in place of the appropriate letters in the equation.
AA=h2(a+b) Substitute 10 for a, 15 for b, and 8 for h.=(8)2((10)+(15))Evaluate piece by piece. 10+15=25 and 82=4.=4(25)=100
Let x=3 and y=−2. Find the value of 3xy+6y−2x.
Evaluate questions 1 through 8, using a=−3, b=2, c=5, and d=−4.
For questions 9 through 11, the weekly cost C of manufacturing x remote controls is given by the formula C=2000+3x, where the cost is given in dollars.
- What is the cost of producing 1000 remote controls?
- What is the cost of producing 2000 remote controls?
- What is the cost of producing 2500 remote controls?
To view the Review answers, open this PDF file and look for section 1.2.