Problem 2 Modeling a Situation

Savings You start with $20 and save $6 each week. What algebraic expression models the total amount you save?

The expression 20 + 6w models the situation.

✓ Got It?

2. You had $150, but you are spending $2 each day. What algebraic expression models this situation?

Problem 3 Evaluating Algebraic Expressions

What is the value of the expression for the given values of the variables?

1. 7 ( a + 4 ) + 3 b − 8  for  a = − 4  and  b = 5 7 open bold italic eh plus 4 close plus 3 bold italic b minus 8 , for , bold italic eh equals negative 4 , and , bold italic b equals 5

   7 ( − 4 + 4 ) + 3 ( 5 ) − 8 Substitute the value for each variable. = 7 ( 0 ) + 3 ( 5 ) − 8 Perform operations within grouping symbols. = 0 + 15 − 8 Multiply. = 15 − 8 Add and subtract from left to right. = 7 table with 5 rows and 2 columns , row1 column 1 , 7 open negative 4 plus 4 close plus 3 open 5 close minus 8 , column 2 cap substitute the value for each variable. , row2 column 1 , equals 7 open 0 close plus 3 open 5 close minus 8 , column 2 cap perform operations within grouping symbols. , row3 column 1 , equals 0 plus 15 minus 8 , column 2 cap multiply. , row4 column 1 , equals 15 minus 8 , column 2 cap add and subtract from left to right. , row5 column 1 , equals 7 , end table

   Plan

   What operations should you start with?

   Do operations that occur in grouping symbols first. Parentheses are grouping symbols.

2. x 2 + y 2  for  x = 1  and  y = 1 2 bold italic x over 2 , plus , bold italic y squared , for , bold italic x equals 1 , and , bold italic y equals , 1 half 1 2 + ( 1 2 ) 2 Substitute the value for each variable .   = 1 2 + 1 4 Simplify the power .   = 3 4 Add . table with 3 rows and 3 columns , row1 column 1 , 1 half , column 2 plus . open , 1 half , close squared , column 3 cap substitutethevalueforeachvariable . . , row2 column 1 , , column 2 equals , 1 half , plus , 1 fourth , column 3 cap simplifythepower . . , row3 column 1 , , column 2 equals , 3 fourths , column 3 cap add . , end table

✓ Got It?

3. 1. What is the value of the expression 2 ( x 2 − y 2 ) 3 fraction 2 . open . x squared , minus , y squared . close , over 3 end fraction  for x = 6 and y = − 3 ? y equals negative 3 question mark
   2. Reasoning Will the value of the expression change if the parentheses are removed? Explain.