## Evaluating expressions

 Suppose you have the variable expression $$\frac{3m-2}{8}$$ This expressions means "I'm thinking of a number that is multiplied by 3, then subtracted by 2, and finally divided by 8." Evaluating an expression means replacing the variable with an actual number. For example, if m = 6, then $$\frac{3m-2}{8}=\frac{3\cdot~6-2}{8}=\frac{18-2}{8}=\frac{16}{8}=2$$

Example 1

 Martha went to the hobby store and purchased two bags of marbles plus 3 extra marbles.

We don't know the number of marbles in each bag, so all we can say is that she bought 2x + 3 marbles.

If we are told there are 42 marbles in each of Martha's bags, then we can substitute 42 for the x in the variable expression.

2x + 3 ------> 2(42) + 3 = 84 + 3 = 87 marbles

Martha bought 87 marbles.

 Example 2 Evaluate $2x+3$ if x = 17. Solution: Replace the variable with 17 and then simplify.

Example 3

 Jenny was filling bottles from a tank of water. When she had filled four bottles with water, 1 cup of water was left in the tank. How much water is in the tank?

The variable expression for this situation is 4c + 1, where c represents the number of cups in each bottle.

If c = 6, how many cups of water are in the tank?

Example 4

If a = 3, b = 6, and c = 4 evaluate each of the following expressions.

 $\large~ab+c$ $\large~\frac{bc}{2}$ $\large~\frac{a(b+4)}{c+1}$

# Self-Check

Question 1

Evaluate $4x-6$ for $x=4$.

Question 2

Evaluate $6x+2x$ for $x=3$.

Question 3

Evaluate $\frac{39}{x}+5y$ for $x=3\mbox{ and }y=5$.