4.9 −0.3
2.7 7.2
 2.5
0.1 − −5.1 0.4 =
−3.8 1.7
4.4
0
 -4
−7 2
=
2 −9
𝐴=
3
5
9
3
−6
9
−5
𝐵=
−3 3
9 −5
−1 4
5 −3 −4
−
=
2 −3
0 4
3
𝐵−𝐴=
New lesson: notes about the equations
Practice
Homework
Missing assignments
Ms. Cardenas
 Solving equation is the process of rewriting the equation to
make what is says about its variable(s) as simple as
possible.
 SWBAT solve one and two step equations.
 SWBAT solve multi-step equations.
 SWBAT solve equations with variables on both sides.
 SWBAT solve literal equations and formulas.
 Equation: is made up of two expressions connected by an equal sign.
Example  2𝑥 + 5 = 7
6x − 2 = 3x + 9y − 4
 Algebraic expression: mathematical phrase that includes 1 or more
variables.
Example  2𝑥 + 5
 Numerical expression: mathematical phrase including numbers and
operations symbols but no variables.
Example 5 + 75 − 23
STEPS:
1. Isolate the variable on one side of the equation.
2. Use the inverse operations (addition/subtraction,
multiplication/division).
3. Whatever we do on one side, we must do it on the other
side.
𝑥 + 5 = 11
𝑥 − 4 = 14
w
= 11
5
𝑎 − 7 = 20
13 = 9 + 𝑚
−15 = −7 + 𝑚
4𝑥 = −32
−3𝑥 = 21
2𝑥 + 6 = 24
5 − 3𝑥 = 35
4𝑥
=8
9
24 = 6 − 6𝑥
𝑥
+ 9 = 14
6
𝑚
18 = − 2
3
 Solving multi-step equations and
variables on both sides
TODAY’S
ACTIVITIES
 Practice
 Solve proportions (grade book)
 Math XL assignment: A1.Multi-step
equations (grade book)
𝑥 − 10 = 7
𝑦 + 8 = −16
10w
= −6
2
𝑥
16 =
+8
−4
STEPS:
1. Remove the parentheses using the distributive property.
2. Combine the variables.
3. Isolate the variable (to keep it positive).
4. When working with fractions, cross multiply or use the
butterfly method.
5. Use the inverse operations.
84 = −7(𝑥 − 4)
3 2𝑥 − 5 + 6 = 5𝑥 + 12
135 = 5 −6𝑎 + 1 + 4𝑎
𝑥 2𝑥 + 3
=
8
5
x 6
=
5 3
𝑥 + 2 10
=
5
7
25 − 7𝑦 = −4𝑦 + 5(5 + 7𝑦)
−7 −2 + 2𝑥 = −8𝑥 − 34
−2𝑚 + 32 = 8 −3𝑚 − 5 − 2𝑚
−2𝑝 + 4𝑝 = −8(1 − 4𝑝)
7 3𝑛 − 1 − 7𝑛 = −38 − 3𝑛
−8 𝑥 − 4 = −4(𝑥 − 6)
 MATH XL  A1.Multi-step
equations (grade book)
TODAY’S
ACTIVITIES
 New topic  Solving equations
“special cases” and rearranging
formulas
 Math XL assignment  A1.Special
cases and rearranging formulas
(grade book)
 We refer to special cases when the variables drop out (the variables
cancel).
 Remove the parentheses if any, and follow the steps learned to solve
the equations.
 If 0 = 0, the solution is true, and the solution is all real numbers.
 If −5 = 0, the solutions is untrue, and we said there is no solution.
0 = 2𝑥 − 2𝑥
−9 + 4𝑦 = −(4 − 4𝑦)
−5𝑥 = 8𝑥 − 8𝑥
−3𝑥 + 2 = −3 1 + 𝑥 + 5
−𝑛 − 3 𝑛 + 6 = 11 − 4𝑛
−3 − 7 1 + 5𝑥 = −7(5𝑥 + 3)
Steps:
 Focus on the specific variable you are solving for.
 Follow the same steps as solving linear equation.
 The answer will NOT have like terms so it will look
“messy”.
Solve for a:
𝑎𝑥 − 𝑏 = 𝑐
Solve for r:
𝐴 = 1 + 𝑟𝑡
Solve for P:
𝐴 = 𝑃(2 + 𝑟𝑡)
Solve for x:
𝑥−𝑦
𝐴=
𝑝
Solve for x:
𝑥ℎ + 𝑥 = 10
Solve for x:
𝑥𝑠 + 𝑥𝑛 = 6
 Math XL assignment  A1.Special
TODAY’S
ACTIVITIES
cases and rearranging formulas
(grade book)
 New topic  Problems using
equations
 Solving equations REVIEW
 A truck can be rented from Company A for ​$120 a day plus ​$0.20 per mile. Company
B charges ​$80 a day plus ​$0.70 per mile to rent the same truck. Find the number of
miles in a day at which the rental costs for Company A and Company B are the same.
 Angie and Kenny play online video
games. Angie buys 2 software packages
and 4 months of game play. Kenny buys
1 software package and 1 month of
game play. Each software package
costs ​$25. If their total cost is ​$135​, what
is the cost of one month of game​ play?
PROBLEM 2
DFA  Tuesday 19th
 −7 3𝑥 + 3 = −21𝑥 + 21
 −3 4𝑥 + 4 = −12𝑥 + 12
 −4 −𝑐 − 24 = −4𝑐 − 24
 −3 −𝑐 − 6 = −3𝑐 − 6
 Solve for b
𝑉=
𝑏−𝑞
𝑦
 Solve for d
𝑁=
𝑑−𝑐
𝑤
 Solve for r
𝑟
2
 Solve for x
𝑥
2
=
𝑟+7
4
=
𝑥+3
8
3
 𝑥
4
− 7 = 10
2
 𝑥
3
+ 10 = 9
2
− 𝑥
5
+8=4
FIRST PART OF
THE CLASS
REVIEW
 Solve the equation. Note if the equation is an identity or if it has no solution.
−4 −𝑐 − 16 = −4𝑐 − 16
 Solve for​ x:
5
− 𝑥
2
− 20 = 20
 Solve the formula for x.
𝑍=
𝑥−𝑚
𝑘
 Solve for m.
𝑚
4
=
𝑚+14
8
SECOND PART OF
THE CLASS
 Math XL  DFA1. 2B Solve
equations
 30 minutes
 NO CELL PHONES!