Evaluate Algebraic Expressions

To evaluate an algebraic expression means to —

replace the variable(s) in the expression with the number value(s) given,
place the given values in parentheses,
simplify the expression using the order of operations, and
determine the end result.

Example 1

Evaluate 4(x² + 5x) − 2y, given that x = 2 and y = -3.

Substitute 2 for x and -3 for y in the given expression:
4[(2)² + 5 · (2)] − [2( -3)]

Simplify using the order of operations:
4[4 + 10] − [-6]
4 [14] − [-6]

56 + 6
62

Example 2

Kinetic energy is given by the formula K = $\frac{1}{2}$ mv². Find the amount of energy when m = 10 kg and v = 6 ^m/_s. (The unit of energy is the Joule.)

Substitute 10 for m and 6 for v in the given formula:

\frac{1}{2}

× (10) × (6)²

Simplify using the order of operations:

\frac{1}{2}

× 10 × 36
5 × 36
180 J

Practice

Substitute the given values for the variables to evaluate each expression.

1) Evaluate 3(x² + 4x) − 3y when x = -5 and y = 3

2) Evaluate x²y for x = -3 and y = -4

3) Evaluate (b − d)² when b = 9 and d = -3

4) Evaluate m⁴ + 2m³ − m² + 8 for m = -2

5) Evaluate y = 3x + 1 for x = -5

6) In baseball, a pitcher's earned run average (ERA) is computed with the expression

\frac{9 r}{p}

, where r is the number of earned runs allowed and p is the number of innings pitched. If a pitcher has allowed 5 earned runs over 12 innings pitched, what is his ERA?

Answers

6) 3.75