CP –Algebra 1
Unit 1- Day 1 Notes
date______________
Targets - Solve Multi-Step Equations
1. I can identify the like terms, coefficients and constant terms.
2. I can solve a multi-step equation (by combining like terms, with variables on both sides, and using inverse
operations) and justify each step.
3. I can translate a word problem into an equation and solve.
GOAL: To solve equations that have both variables and whole numbers on each side of the equation (equal sign).
Inverse operations will be used to move the necessary variable and whole number to the needed side of the
equal sign so that the variable will be on one side, and the whole numbers (without variables) will be on the
other side. For example, x = 4.
Warm-Up: Solve the following one-step equations.
a. 6 = 9 + h
b. x - 7 = 4
𝑐
d. 6 =
c.
𝑡
e. − 3 = 9
7
6w = -54
f.
5
6
𝑤 = 10
Steps to solve a two-step equation
1)
Use the inverse operation to isolate the variable (i.e. move the terms with variables to one side
of the equation)
2)
Use the inverse operation to solve for the variable.
Solve an equation by using inverse operations to isolate the variable
Solve 5x – 5 = 10
Steps
5x – 5 = 10
+5 + 5
5x = 15
5
5
Justification
Use inverse operation of adding 5 to both sides to get the variable
Use inverse operation of dividing by 5 on both sides to get x by
itself
x =3
Ex. 1 Solve each equation
a.
d.
𝑥
2
+ 5 = 11
b. 5x + 9 = 24
2
e. 2 − 9 = 11
10 = 7 𝑛 + 4
𝑏
c.
16 = 4y – 4
f.
10 = 7 − 𝑚
CP –Algebra 1
Unit 1- Day 2 Notes
date______________
Targets - Solve Multi-Step Equations
1. I can identify the like terms, coefficients and constant terms.
2. I can solve a multi-step equation (by combining like terms, with variables on both sides, and using inverse
operations) and justify each step.
3. I can translate a word problem into an equation and solve.
Solve a two-step equation by first combining like terms and second using inverse
operations
Solve 7𝑥 − 4𝑥 = 21
Steps
7x – 4x = 21
3x = 21
3
3
x=7
Ex. 2
a.
6𝑝 − 2𝑝 = 28
Warm-Up:
Justification
Combine like terms (7x – 4x)
Use inverse operation of dividing by 3 on both sides to get x by
itself
b.
6𝑥 + 3𝑥 = 36
5
1
c. 8 = 8 𝑦 − 8 𝑦
Simplify each expression by combining like terms
a.
2x  7x
b.
4a  8a
c.
6x  8x  3x
d.
4x  5  6x  2
e.
3x  10  3  11x
f.
8  5x  2x  12
Steps to solve a multi-step equation
1)
Simplify one or both sides of the equation
2)
Then use inverse operations to isolate variable and justify.
Solve an equation by combining like terms and justify Solve
Steps
Justification
3x + 5x – 5 = 11
8x – 5 = 11
5 +5
8x = 16
8
8
x =2
Ex 1
combine like terms on each side of the equal sign
use inverse operation of adding 5 to both sides to get
the variable alone on one side of the equal sign
use inverse operation of dividing by 8 to get x by itself
Solve each equation and justify each circled problem.
a.
2x  7x  3  12
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b.
5x  x  7  17
c.
10  2x  8  5x
Solve an equation with variable on both sides and justify Solve 2x  3  x  2x  7
Steps
Justification
2x + 3 + x = 2x + 7
3x + 3 = 2x + 7
- combine like term
-2x
-2x
- inverse operation of subtracting 2x from both sides to move
x+3=7
the variable to one side of the equal sign
-3 -3
- inverse operation of subtracting 3 from both sides to move
the whole number (number without a variable) to the OTHER
x =4
side of the equal sign
‘
Ex 2
Solve each equation and justify each circled equation.
a.
7x  4  3x  12
b.
7 x  5  2x  23
c.
x  5  4x  2x  10
d.
2
x  14
3
e.
1
x 5  3
2
f.
1
2x  x  8
2
g.
3
x 2  x 3
4
h.
5
x  2  3x
2
Ex 3 The perimeter of a triangle is 22 feet. The side lengths are x, 3x and 6 ft. Write an equation and
solve for x.
Ex 4
The length of a rectangle is 4 units more than 2 times the width. The perimeter is 32 units. Find
the length and width of the rectangle described.