#### Lesson 3.1 Solving Two

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Lesson 3.1 Solving Two

Essential Question: How do you
solve equations with variables on
both sides?
Before we
start…
David has $26 and saves $8 each week. Emily has
$56 and saves $4 each week. How many weeks will
it take for David and Emily to have the same
amount of money?
Variables on Both Sides of the
Equation
Continue to use
inverse operations to
isolate the variable.
Collect variable terms
on side and constant
terms on the other side
How do I solve an equation with variables
on both sides?
• Simplify expressions on both sides of the equation.
• Collect all variable terms on one side of the equation.
• Collect all constant terms on the other side of the
equation.
• Use inverse operations to isolate the variable.
Solve 7𝑛 − 5 = 10𝑛 + 13
Solve 5𝑛 − 2 = 3𝑛 + 6
Solve 8𝑦 + 4 = 11𝑦 − 17
Solve 𝑚 − 1 = 9𝑚 + 15
Solve 5 2𝑥 + 1 = 10𝑥
Solve 6𝑥 + 2 = 2 3𝑥 + 1
Solve 3𝑥 − 7 = 8 + 6 𝑥 + 2
Solve 13𝑦 + 19 = 6 9 + 𝑦 + 14
Solve 8 𝑧 + 4 = 5 13 + 𝑧
Solve 8𝑎 − 2 𝑎 + 5 = 2 𝑎 − 1
Solve 4 −2 + 3𝑥 = 12𝑥
Solve 7 2𝑥 + 3 = 21 + 14𝑥
Spanish Club The Spanish club is arranging a trip to a
Mexican restaurant in a nearby city. Those who go must
share the $60 cost of using a school bus for the trip. The
restaurant’s buffet costs $5 per person. How many
students must sign up for this trip in order to limit the
cost to $10 per student?
Tour Bus A bus tour of celebrities’ homes costs $300
for the bus and tour guide plus $8 per person for lunch.
How many people does a tour group need to have in it
so that the cost per person is $20?
Shopping You spend $60 on clothes and buy 3 DVD
movies. Your friend spends nothing on clothes and buys
8 DVD movies. You both spend the same amount of
money. All the DVDs cost the same amount. How much
does each DVD cost?
How do you solve equations with variables on
both sides?
Ticket Out the Door
Solve
2𝑥 − 6 = 4 5𝑥 + 12