Download Define a variable and write an algebraic expression for each phrase:

Ahrens 1
7R: Two-Step Equations
Define a variable and write an algebraic expression for each phrase:
(a) five years more than three times your age
Let a = your age in years
(b) seven centimeters less than twice the span of your hand
Let h = the span of your hand
(c) ten people fewer than half the population of your town
Let p =
Two-Step Equations
Rules to isolate the variable:
1. you undo addition and subtraction
2. you undo multiplication and division
Example:
2w + 3 = 9
-3 -3 → undo addition by subtracting 3 on both sides
2w
=6
2w
2
= 6 → now you have this
2 → undo multiplication by dividing by 2 on both sides
w
= 3
Check:
2w + 3 = 9
?
2(3) + 3 = 9
6 +3= 9
9 = 9√
Ahrens 2
7R: Two-Step Equations
You Try: Think – what do you have to undo first?
(a) 3x – 10 = 8
(b) 8d + 5 = 45
(c) 4y – 11 = 33
1. Grandma sends you 5 video games for your birthday. The games all have
the same weight. The box she mails them in weights 8 ounces. The total
weight is 48 ounces. Can you solve the problem to find the weight of each
video game?
Let g = weight of game
IN WORDS
Total Weight = Weight of 5 video games + weight of box
IN NUMBERS
2. During the first half of the basketball game you scored 8 points. In the
second half you made only 3-point baskets. You finished the game with 23
points. Write and solve an equation to find out how many 3-point baskets
you made.
Let t =
3. An electrician charges a fee to come to your house in addition to an hourly
rate. This can be modeled by 40h + 35 = 115. Explain what each part of the
equation represents. Then solve the equation to find the number of hours the
electrician works.