Understanding
Equations
7th Grade
Module 3
Lesson 7
Vocabulary:
 Equation:
An equation is a statement of
equality between two expressions.



Has an “=“ in it.
Represents a complete thought- a
sentence.
Examples:
3
+4=7
 4x – 5(6x + 2)=32
Vocabulary:
 Number
Sentence: A number sentence is
a statement of equality (or inequality)
between two numerical expressions.



Only numbers, no variables
Always true or always false.
Examples:
 15
+ 28 = 43
 10(5) – (100 ÷ 10) = 40
Vocabulary:
 Solution:
A solution to an equation with
one variable is a number that, when
substituted for all instances of the variable
in both expressions, makes the equation a
true number sentence.
Opening Exercise

Your brother is going to college so you no longer have
to share a bedroom. You decide to redecorate a wall
by hanging two new posters on the wall. The wall is 14
feet wide, and each poster is four feet wide. You want
to place the posters on the wall so that the distance to
the edge of each poster to the nearest edge of the wall
is the same as the distance between the posters, as
shown in the diagram. Determine the distance.
Opening Exercise

Your brother is going to college so you no longer have to share a bedroom. You
decide to redecorate a wall by hanging two new posters on the wall. The wall is 14
feet wide, and each poster is four feet wide. You want to place the posters on the
wall so that the distance to the edge of each poster to the nearest edge of the wall
is the same as the distance between the posters, as shown in the diagram.
Determine the distance.
Opening Exercise

Your parents are redecorating the dining room
and want to place two rectangular wall sconce
lights that are 25 inches wide along a 10 2/3 feet
wall so that the distance between the lights and
the distances from each light to the nearest edge
of the wall are all the same. Design the wall and
determine the distance.
Opening Exercise

Your parents are redecorating the dining room and want to place two rectangular
wall sconce lights that are 25 inches wide along a 10 2/3 feet wall so that the
distance between the lights and the distances from each light to the nearest edge
of the wall are all the same. Design the wall and determine the distance.
Opening Exercise

Let the distance between a light and the nearest edge
of a wall be x ft. Write an expression in terms of x for the
total length of the wall. Then use the expression and the
length of the wall given in the problem to write an
equation that can be used to find that distance.
Opening Exercise

Now in inches: Let the distance between a light
and the nearest edge of a wall be y inches. Write
an expression in terms of y for the total length of
the wall. Then, use the expression and the length
of the wall to write an equation that can be used
to find that distance (in inches).
3y + 50 = 128
What values of y makes the second
equation true: y = 24, y = 25, or y = 26?
Example
 The
ages of three sisters are consecutive
integers. The sum of their ages is 45.
Calculate their ages.
a.
Use a tape diagram to find their ages:
x
x
1
x
1
45
1
Example
b.
If the youngest sister is x years old, describe the
ages of the other two sisters in terms of x, write
an expression for the sum of their ages in terms
of x, and use that expression to write an
equation that can be used to find their ages
Example
c.
Determine if your answer from part (a) is a
solution to the equation you wrote in part (b)
(a)
(b)
14
3x + 3 = 45
Exercise
 Sophia
pays a $19.99 membership fee for
an online music store.
a.
If she also buys two songs from a new
album at a price of $0.99 each, what is
the total cost?
Exercise
b.
If Sophia purchases n songs for $0.99
each, write an expression for the total
cost.
Exercise
c.
Sophia’s friend has saved $118 but is not sure
how many songs she can afford if she buys the
membership and some songs. Us the expression
in part b to write an equation that can be used
to determine how many songs Sophia’s friend
can buy.
Exercise
d.
Using the equation written in part c, can
Sophia's friend buy 101, 100 or 99 songs?
Summary
 An
equation can be written from an
expression by making the expression
equal to something.
 To determine if a number is a solution to
an equation you need to plug that value
into the equation for the variable and see
if the equation is true.
Exit Ticket
 Homework
is the problem set to lesson 7