The document outlines learning objectives for a lesson on solving various types of equations and inequalities. Students will learn to: 1) recognize forms of linear and quadratic equations; 2) solve linear, quadratic, and simultaneous equations through methods like factorization, quadratic formula, and substitution/elimination; and 3) identify and solve inequalities in forms like interval and set notation. Examples of solving different equation types are provided.

2. At the end of this lesson, student should be
able to:
• Recognize the general form for linear
equations
• Solve the linear equations
• Recognize the general form for quadratic
equations
• Solve quadratic equations using the
technique of factorization, quadratic formula
and completing the square
• Solve simultaneous equations for 2 x 2
systems using substitution and elimination
methods
• Identify the notation of inequalities and
properties of inequalities
• Express the solution in inequality notation,
real number line, interval notation or sets
notation
• Solve linear inequalities
• Identify the absolute value
• Solve the absolute value equations

6. 1. y=
𝒙+𝟏𝟐
𝟓
2. y=
𝟕−𝒙
𝒙
3. y=𝟑𝒙𝟐
+ 𝟏
 y=
𝒙
𝟓
+
𝟏𝟐
𝟓
 LINEAR
 y=
𝟕
𝒙
-
𝒙
𝒙
 y=
𝟕
𝒙
-1  xy=7-1 NOT
LINEAR
 NOT LINEAR

7. 5x-2+2=3x+8+2
5x=3x+10
5x-3x=10
2x=10
x=5
2x-2+x=10x+15
2x+x-10x=15+2
-7x=17
x=
−𝟏𝟕
𝟕
=-2
𝟑
𝟕

10. 𝟔 𝟐𝒙 −𝟏𝟓(𝒙−𝟕)
𝟑𝟎
=
𝟏𝟎(𝟕)
𝟑𝟎
𝟏𝟐𝒙−𝟏𝟓𝒙+𝟏𝟎𝟓
𝟑𝟎
=
𝟕𝟎
𝟑𝟎
−𝟑𝒙+𝟏𝟎𝟓
𝟑𝟎
=
𝟕𝟎
𝟑𝟎
−𝟑𝒙
𝟑𝟎
=
𝟕𝟎
𝟑𝟎
-
𝟏𝟎𝟓
𝟑𝟎
−𝟑𝒙
𝟑𝟎
= -
𝟑𝟓
𝟑𝟎
-90x=-1050
x= 11.67= 11
𝟔𝟎
𝟗𝟎
= 11
𝟐
𝟑

11. 3y-5x=7x-14y
3y+14y=5x+7x
17y=12x
y=
𝟏𝟐𝒙
𝟏𝟕
=
𝟏𝟐
𝟏𝟕
x

12. 7y+3x=2(21)
7y+3x=42
7y= -3x+42
y=
−𝟑𝒙
𝟕
+6

13. 2y=3x
𝟐𝒚
𝟑
= 𝒙

14. n= -4m+2=-4(1)+2=-4+2=
-2
2m-3n=8
2m – 3(-4m+2)=8
2m +12m -6 =8
14m-6=8
14m=8+6
14m=14
3(4m+n=2)12m+3n=6-------
3
2m - 3n=8
12m+3n=6
-------------------------
14m=14
m=1
4m+n=24(1)+n=2n=-4+2

15. 2y+7x= -5---------------------
-1
2(1)+7x=-5
2+7x=-5
7x=-5-2
7x=-7
x=-1
2y+7x= -5---------------------
-1
5y-7x=12---------------------
--2
--------------------
7y=7
y=1

21. Completing the
Square
(x+3) (x+1)
x+3=0
x+1=0
x= -3 x= -
1
𝒙𝟐 + 𝟒𝒙 = −𝟏
𝒙𝟐 + 𝟒𝒙 + (
𝟒
𝟐
)𝟐= −𝟏+ (
𝟒
𝟐
)𝟐
𝒙𝟐
+ 𝟒𝒙+4=-1+4
𝒙𝟐
+ 𝟒𝒙+4=3
(𝒙 + 𝟐)𝟐=3
(𝒙 + 𝟐)𝟐= 𝟑
x+2=± 𝟑 𝒙𝟏=-2+1.73=-
0.27
5𝒙𝟐 − 𝟒𝒙 = 𝟐
𝒙𝟐 − 𝟎. 𝟖𝒙 + −
𝟎.𝟖
𝟐
𝟐
= 𝟎. 𝟒+ (−
𝟎.𝟖
𝟐
)𝟐
𝒙𝟐 −0.8x+0.16 = 0.4+0.16
𝒙𝟐 −0.8x+0.16 = 0.56
(𝒙 − 𝟎. 𝟒)𝟐=0.56
(𝒙 − 𝟎. 𝟒)𝟐= 𝟎. 𝟓𝟔
x-0.4=± 𝟎. 𝟓𝟔 𝒙𝟏=0.4+0.75=1.15
x=0.4 ± 𝟎. 𝟓𝟔 𝒙𝟐=0.4-0.75=-0.35

22. a=2; b=-5, c=1
x=
−(−𝟓)± (−𝟓)𝟐−𝟒(𝟐)(𝟏)
𝟐(𝟐)
x=
𝟓± 𝟐𝟓−𝟖
𝟒
x=
𝟓± 𝟏𝟕
𝟒
𝒙𝟏=
𝟓− 𝟏𝟕
𝟒
= 0.22
𝒙𝟐=
𝟓+ 𝟏𝟕
𝟒
= 2.28

37. 𝑥1= =
−𝟒+ 𝟒𝟎
𝟒
= 0.58
𝑥2= =
−𝟒− 𝟒𝟎
𝟒
= -2.58

38. 𝑥1= =
𝟒+ 𝟏𝟏𝟐
𝟔
= 2.43
𝑥2= =
𝟒− 𝟏𝟏𝟐
𝟔
= -1.10

44. Factori
ng