Evaluate Algebraic Expressions

Evaluate Algebraic Expressions

To evaluate an algebraic expression means to —

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(x**

^{2}+ 5x) − 2y, given that x = 2 and y = -3.Substitute 2 for x and -3 for y in the given expression:

4[(2)

Simplify using the order of operations:

4[4 + 10] − [-6]

4 [14] − [-6]

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*=*mv*^{2}. Find the amount of energy when*m*= 10 kg and*v*= 6^{m}/_{s}.*(The unit of energy is the Joule.)*

Substitute 10 for

× (10) × (6)

Simplify using the order of operations:

× 10 × 36

5 × 36

*m*and 6 for*v*in the given formula:× (10) × (6)

^{2}Simplify using the order of operations:

× 10 × 36

5 × 36

180 J

180 J

Practice

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

1) Evaluate 3(x^{2} + 4x) − 3y when x = -5 and y = 3

2) Evaluate x^{2}y for x = -3 and y = -4

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

4) Evaluate m^{4} + 2m^{3} − m^{2} + 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 , 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

Answers

6)

**3.75**