The document provides examples and steps for solving algebraic expressions and equations. It includes examples of simplifying expressions, evaluating expressions given variable values, solving equations using transposition methods, determining if a given variable value makes an equation true, and combining like terms. The examples cover topics like evaluating expressions, solving one-step equations, determining variable values that make statements true, and combining algebraic expressions.

1. Solving Problems
Involving Algebraic
Expressions and
Equations

2. Learning Target:
c. solve routine and non-routine
problems involving different
types of numerical expressions
and equations;
a. simplify an expression;
b. evaluate algebraic expressions;

4. Give the value of
each symbol based
on the equation.

5. + 4 =
10
Give the value of each symbol based
on the equation.
=
_____
6

6. x 8 =
56
Give the value of each symbol based
on the equation.
=
_____
7

7. =
48
Give the value of each symbol based
on the equation.
=
_____
2
4
+

8. ÷ 9 = 5
Give the value of each symbol based
on the equation.
= ___
45

9. ÷ 2+ 2
= 27
Give the value of each symbol based
on the equation.
=
____
50

10. A car park in a mall charges ₱30.00 for
the first hour plus ₱5.00 for every
succeeding hour for parking fee. How
much is the fee for a car parked in the
mall for 6 hours?
To solve the problem, we apply our knowledge on how to translate verbal
expression to algebraic expression.
Ralph pays a fix amount of ₱30.00 for the first hour and pays (x-
1) hours of ₱ 5.00 per hour.
Let’s
Translate:
Let’s
Substitute:x =6
SOLUTION
:
5(x-1) +
30
5(x-1) + 30
5(6-1) + 30
5(5) + 30
25 + 30 =

11. The value of an algebraic expression
can be evaluated if the value of the
variable is known.
This is how we find its value:
Find x + 5 if x
= 45
SOLUTI
ON:
x + 5
= 50
= 45 + 5Substitute 45 to x.
Add.

12. The value of an algebraic expression
can be evaluated if the value of the
variable is known.
This is how we find its value:
What is y – 3 if
y = 18
= 18 - 3
SOLUTI
ON:
y - 3
= 15
Substitute 18 to y.
Subtract.

13. The value of an algebraic expression
can be evaluated if the value of the
variable is known.
This is how we find its value:
If a = 3.2, find
2a
= 2
(3.2)
SOLUTI
ON:
2a
= 6.4
Substitute 3.2 to a.
Multiply.

14. The value of an algebraic expression
can be evaluated if the value of the
variable is known.
This is how we find its value:
Evaluate 100
d
= 100
5
SOLUTI
ON:
100
d
= 20
Substitute 5 to d.
Divide.
gives that d = 5

16. Determine if the given value of the variable makes the
equation true.
Write T if the equation is true. Otherwise, write F.
5x + 4 = 1
x = 1

17. Determine if the given value of the variable makes the
equation true.
Write T if the equation is true. Otherwise, write F.
3a - 2 = 4
a = 2

18. Determine if the given value of the variable makes the
equation true.
Write T if the equation is true. Otherwise, write F.
r - 7 = 1
r = 6

19. Determine if the given value of the variable makes the
equation true.
Write T if the equation is true. Otherwise, write F.
4s + 1 =
13
s = 3

20. Determine if the given value of the variable makes the
equation true.
Write T if the equation is true. Otherwise, write F.
2x - 2 = 5
x = 7
2

22. Determine the number that can
replace the letter to make each
mathematical statement true.
x + 7 =
18
22
11
5
23

23. Determine the number that can
replace the letter to make each
mathematical statement true.
n - 5 =
23
28
18
29
17

24. Determine the number that can
replace the letter to make each
mathematical statement true.
c - 8 =
10
24
18
27
28

25. Determine the number that can
replace the letter to make each
mathematical statement true.
t - 10 =
50
60
30
90
70

26. Determine the number that can
replace the letter to make each
mathematical statement true.
3d = 39
12
13
10
14

27. Determine the number that can
replace the letter to make each
mathematical statement true.
3p = 15
6
7
5
4

28. Determine the number that can
replace the letter to make each
mathematical statement true.
t
2
70
75
74
72
= 36

29. To combine like terms, add or
subtract their numerical coefficients
and write the result with the common
literal coefficient.
a + a + a
=
2b + b =
3c + 2c +
c =
8d – 3d =
y + y + y
+ y =
10h – 6h +
4h =
6i + 6i –
6i =
4e + 5e –
e =
3
a
3
b 6
c
5
d
4
y
8
h
6i
8
e

30. Determine if the given value of the variable makes the
equation true.
Write T if the equation is true. Otherwise, write F.
4s + 1 =
13
s = 3

31. Determine the number that can
replace the letter to make each
mathematical statement true.
3p = 15
6
7
5
4

32. Determine if the given value of the variable makes the
equation true.
Write T if the equation is true. Otherwise, write F.
2x - 2 = 5
x = 7
2

33. Solving Simple Equations Using Transposition Method
4n + 9 = 21
SOLUTI
ON:
4n + 9 =
21 4n = 21
- 9
Transpose 9 to the right
side, and then use the
opposite operation.
4n = 12 Transpose 4 to the right
side, and then use the
opposite operation.
n = 12
÷ 4
n = 3
Subtract 9 from 21.
Divide 12 by 4.

34. 5y - 4 = 26
SOLUTI
ON:
5y – 4 =
26 5y = 26
+ 4
Transpose 4 to the right
side, and then use the
opposite operation.
5y = 30
5
5
y = 6
Add 26 and 4.
Divide both sides by 5.
5y = 30
Solving Simple Equations Using Transposition Method

35. Solving Simple Equations Using Transposition Method
6x – 4 = 2x
+ 8
SOLUTI
ON:
6x – 4 = 2x
+ 8
6x – 2x = 8
+ 4
Transpose 4 to the right side, and
then use the opposite operation.
Subtract 6x and 2x.
4x = 12
4 4
x = 3 Divide both sides by 4.
Transpose 2x to the left side, and
then use the opposite operation.
Add 8 and 4.
4x = 12