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Essential Question: How do you
solve equations with variables?
Before we
start…
Which of the following
would be considered an
equation?
3x  7
16  4 x  4
What is an equation?
A mathematical sentence
formed by placing an
equal sign, =, between
two expressions.
𝑥 + 8 = 12
What is a solution?
A number that
produces a true
statement when it is
substituted for the
variable.
How do you write verbal sentences as
equations?
• To write a verbal sentence as an equation you
will translate words into operations and
mathematical symbols.
• The word is represents an equal sign.
Write as equations.
The sum of x and 6 is 9.
The difference of 12 and y is 15.
Write as equations.
The product of −4 and p is 32.
The quotient of n and 2 is 9.
Write as equations.
The sum of 3 and z is −10.
The quotient of m and 6 is 4.
Write as equations.
The difference of x and 8 is −4.
The sum of 26 and y is 43.
The quotient of p and 7 is 16.
The product of 14 and m is 56.
How do you check to see if a number
is a solution?
• You substitute the number in for the variable
and see if it produces a true statement.
Tell whether 9 or 7 is a solution of x  5  2
x
Tell whether 52 or 60 is a solution of  13
4
Tell whether  6 or 3 is a solution of x  9  12
Tell whether 13 or 9 is a solution of 91  7c
What about solving equations?
• Solving the equation is finding all solutions
of an equation.
• You can use mental math to solve a simple
equation by thinking of the equation as a
question.
How can you solve equations with
variables?
• Some equations can be solved by using mental
math.
Using Mental Math
• Some equations are simple enough to solve
using mental math.
• Think of the equation as a question.
• Once you answer the question, check the
solution.
4. x  10  7
5. 2  n  6
6. 3w  15
36
7. 4 
s
From 1998 to 2002, biologist Jane Shen-Miller grew
several lotus plants from ancient seeds she found in
China. The oldest seed was about 500 years old.
Estimate the year when this seed was formed.
Go-cart rides cost $5 each at a county fair. During the
first day of the fair, the go-cart operator takes in a total
of $1000. How many times did people ride the go-carts
that day? Write and solve an equation to find the
answer.
The dragonfly is the fastest flying insect. It can move at
a speed of 50 feet per second. Find the approximate
time it takes a dragonfly to travel 400 feet. Write and
solve an equation.
You divide a bag of trail mix into 8 portions for you and
your friends to have as snacks on a bike ride. Each
portion weighs 3 ounces. Find the total weight of the
trail mix originally in the bag. Write and solve an
equation.
How do you solve equations with variables?
Ticket Out the Door
Solve the equation using mental math.
7 x  63