Here are the key steps to solve word problems involving linear equations: 1. Read the problem carefully and identify the important details. 2. Define variables to represent unknown quantities. 3. Write a mathematical expression relating the variables based on the context of the problem. 4. Form an equation and solve it using proper order of operations. 5. Check that the solution makes sense in the context of the original problem.

1. By : Mr Ronald Naradus S
SMPK PENABUR GADING SERPONG

2. Glossary EQUATIONS AND
INEQUALITIES IN
ONE VARIABLE
Inequalities
Mathematics
Sentence Equations
Definition
Solving
Statement Equation
Properties
Inequalities
Properties
Open
Equation
Sentence
Closed Solving
Definition
Sentence Inequalities

3. Open sentence = kalimat terbuka
Closed sentence = kalimat tertutup
Open mathematical sentence = kalimat matematika terbuka
Equation = persamaan
Side = ruas
Member = suku, bagian
Equation of one variable = persamaan satu peubah
Linear equation of one variable = persamaan linear satu variabel
First-degree equation, equation of degree one = persamaan berderajat satu
Solution of the equation = penyelesaian persamaan
Solution set = himpunan penyelesaian
Equivalent equations = persamaan yang ekuivalen
Inequality = pertidaksamaan
Inequality of one variable = pertidaksamaan satu variabel
Linear inequality of one variable = pertidaksamaan linier satu variabel
Interval = interval, selang

4. STATEMENTS
1. The prime numbers are
always odd number
2. Stanley is a great student

5. What is the
different between
both sentence?

6. Statements
Statement means any
sentences that can be
determined for its value of truth (
either true or false ) but not both
values

7. State weather the following are true or false !
a. The number of players in a football team is 12. F
b. 2 is not prime number
F
c. 21+15 35 T
d. -20 -19 F
e. A negative number plus a negative number is a
positive number F
f. Medan is capital of west sumatera province F
g. The sun arises from west
F
h. 2+3=6 F

8. The following are not
examples of statements
a. Have you learnt mathematics ?
b. Study hard
c. Durian’s taste is very delicious
d. Trader is rich person
e. The girl is very attractive

9. *
Is the sentence “ y is a person who was
Indonesian president “ true or false ?
If y replaced by Ir. Soekarno, then the
sentence becomes a statement having
true value
While if y is replaced by Hitler, then the
sentece becomes an a statement having
false value

11. An open sentence is a
sentence which cannot
be determined whether
it is a correct or
incorrect sentence.

12. A closed sentence is
a correct or incorrect
sentence.

14. EXAMPLE
o minus to 33 equal to 11
( open sentence )
o = 44 ( solution )
o 44 minus to 33 equal to 11
( Closed sentence )

15. DO EXERCISE 32
PAGE 49 NO. 1 - 3

16. APPLICATION OF LINEAR EQUATION IN DAILY LIFE
the following are several terms commonly used in narrative problem
and how to write them.
NO Terms How to Write
1 The sum of m and n m+n
2 The difference between m and n, m > n m–n
3 The sum of the square of m and n m2 + n2
4 The square of the sum of m and n (m + n)2
5 The difference between the square of m and n, m > n m2 – n2
6 The squared of of the difference of m and n , m > n (m – n )2
7 The opposite of m -m
8 The reciprocal of m
9 The sum of reciprocal of m and n
10 The reciprocal of the sum of m and n
11 The product of m and n mn

17. Equations
Equation is an open
mathematical sentence which
contains an equality sign “ = “

18. Linear Equations
 A linear equation in the variable x is an equation that can be written in
the form
ax + b = 0
where a is coefficients, b is constants and a ≠ 0.
 A linear equation is also called a first-degree equation or an equation of
degree one.
 3x − 7 = 0 and 5x = 25 are linear equations.

19. Solving an Equation

20. Three Operations

21. How do we solve equations with inverse
operations?
• Let’s take a look at a simple equation
Step 1: x 13 21 Now that we have solved the
equation, let’s check the solution:
- 13 - 13
Answer: x 8
x 13 21
8 13 21
21 21

22. HOW DO WE SOLVE EQUATIONS WITH
INVERSE OPERATIONS?
Let’s take a look at a simple equation
Step 1: y 5 12 Now that we have solved the
equation, let’s check the solution:
+5 +5
Answer: y 17 y 5 12
17 5 12
12 12

23. HOW DO WE SOLVE EQUATIONS WITH
INVERSE OPERATIONS?
Let’s take a look at a simple equation
Step 1: 25W 75 Now that we have solved the
equation, let’s check the solution:
25 25
75 25W 75
Step 2: W
25 25(3) 75
Answer: W 3 75 75

24. How do we solve equations with inverse
operations?
• Let’s take a look at a simple equation
A Now that we have solved the
Step 1: (16) 4 (16) equation, let’s check the
16 solution:
A
4
Step 2: A 4(16) 16
64
4
Answer: A 64 16
4 4

25. 1 Step Equation
1
X + 11 = 9 X - 37 = 52 3X = 72
-11 -11 13 3
X = -2 X = 24
20 + h = 41 17 - s = 27

26. 1 Step Equations Continued…
6X = 42 X/7=4 X / 5 = 10
3 / s = 21 2P=3
5 4

27. Multi Step Equations
w 17 31
Solve:
6
8m – 10 = 36
8m – 10 = 36
+ 10 + 10
8m = 46
8 8
m = 23
4

28. Multi Step Equations
Notice that there are
Solve: 5x 2=x+4 variables on both sides
5x 2=x+4 Get rid of the -2
+2 +2
on the left side
5x = x + 6
Simplify
5x =–x + 6
–x x Get rid of the x
on the right side
4x = 6
Simplify
4 4 Get rid of the
coefficient of x
x =3 Simplify
2

29. Solving a Proportion
• Solve the proportion below
6 12
6(60) C (12)
C 60 360 12C
12 12
30 C

30. Solving a Proportion
• Solve the proportion below
13 a
13(8) 52(a)
52 8
104 52a
52 52
2 a

31. Checking the Solution to a Proportion
• Let’s check the solution to the proportion we
solved on the last slide
13 a 13 2
52 8 52 8
1 1
4 4

32. Using Proportions to Solve Problems
• You get 46 miles to a gallon of gas. How far
can you go on 16 gallons of gas?
1 16
1m 46(16)
46 m m 736

33. APPLICATION OF LINEAR EQUATION IN DAILY LIFE
the following are several terms commonly used in narrative problem
and how to write them.
NO Terms How to Write
1 The sum of m and n m+n
2 The difference between m and n m–n
3 Product of m and n mxn
4 Quotient of m and n m:n
5 The inverse of m
6 Inverse of the sum of m and n
7 Square of sum of m and n ( m + n )2
8 Sum of square of m and n m2 + n2
9 Square of difference m and n (m – n )2
10 Difference of square of m and n, m2> n2 m2 – n2
11 Square of m m2