EQUATIONS TOPIC

1. WELCOME TO OUR CLASS!

2. An equation is a statement of
equality between two expressions
called members.

3. Parts of an Equation
8 + 3 = 11
5𝑥5 = 25
50
50
+
50
50
= 2
100 − 88 = 12
25 − 36 = −1
Examples:

4. It typically involves variables, which are
often represented by letters, and the goal
is to find the values of the variables.
Conditional Equation

5. Parts of an Equation
2𝑥 + 3 = 9
3𝑦 − 7 = 8
2
3
𝑥 = 4
𝑧 − 1 + 2 = 5
Examples:

6. Also known as valid inputs, refer to the
set of values that can be assigned to a
variable in a given mathematical
equation.
Permissible Values

7. example:
𝑥 = 4; 𝑥 = −4
𝑥2
= 16
𝑥2 = 16 𝑥2 = 16
Permissible Values
4 2
= 16
16 = 16
−4 2
= 16
16 = 16

8. The solutions of a conditional equation are those values of
the unknowns which make both members equal. These
solutions are said to satisfy the equation. If only one
unknown is involved the solutions are also called roots. To
solve an equation means to find all of the solutions.
solution

9. 1). If equals are added to
equals, the results are equal.
Thus if x – y = z, we may
add y to both members and
obtain x = y + z
Operations used in transforming equations
𝑥 − 𝑦 = 𝑧
5−3 = 2
2 = 2
5 = 3 + 2
5 = 5

10. 2. If equals are subtracted
from equals, the results are
equal.
Thus if x+2 = 5, we may
subtract 2 from both members
to obtain x = 3.
Operations used in transforming equations
𝑥 + 2 = 5
𝑥 + 2 − 2 = 5 − 2
𝑥 = 3

11. 3) If equals are multiplied by
equals, the results are equal.
Thus if both members of
1
5
𝑦 = 2𝑥2 are multiplied by 5
the result is 𝑦 = 10𝑥2
Operations used in transforming equations
1
5
𝑦 = 2𝑥2
1
5
(10𝑥2) = 2𝑥2
2𝑥2 = 2𝑥2
5(2𝑥2
) = 5 2𝑥2
10𝑥2 = 10𝑥2

12. 4. If equals are divided by
equals, the results are equal
provided there is no division
by zero.
Thus if -5x = -20, we may
divide both members by -5 to
obtain x = 4.
Operations used in transforming equations
−5𝑥 = −20
−5𝑥
−5
=
−20
−5
x = 4
-20 = -20
−5(4) = −20

13. (𝑥 + 5)(𝑥 − 9)
𝑓𝑎𝑐𝑡𝑜𝑟𝑠:
−5 1 -4 -45
−5 1 -5 45
−5 1 -9 0
𝑟𝑜𝑜𝑡𝑠 ∶ 𝑥 = −5 ; 𝑥 = 9
𝑥 − 9
𝑥 − 9 = 0
𝑥 = 9

14. (𝑥 + 3)(𝑥 − 2)(x − 2)
𝑓𝑎𝑐𝑡𝑜𝑟𝑠:
−3 1 -1 -8 12
𝑟𝑜𝑜𝑡𝑠 ∶ 𝑥 = −3 ; 𝑥 = 2
𝑥2
− 4𝑥 + 4
(𝑥 − 2)(𝑥 − 2)
𝑥 = 2
−3 1 -3 12 -12
−3 1 -4 4 0

15. 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥:
3 𝑥 + 2 = 2 𝑥 − 3 + 5
Type equation here.
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 3. 3 𝑥 + 2 = 2 𝑥 − 3 + 5
3𝑥 + 6 = 2𝑥 − 6 + 5
3𝑥 + 6 = 2𝑥 − 1
3𝑥 − 2𝑥 = −6 − 1
3 𝑥 + 2 = 2 𝑥 − 3 + 5
𝑐ℎ𝑒𝑐𝑘𝑖𝑛𝑔:
3 −7 + 2 = 2 −7 − 3 + 5
3 −5 = 2 −10 + 5
−15 = −20 + 5
−15 = −15
𝑥 = −7

16. Type equation here.
𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑥 𝑣𝑎𝑙𝑢𝑒:
𝐸𝑥𝑎𝑚𝑝𝑙𝑒 4.
1
𝑥
= 8 −
3
𝑥
𝑐ℎ𝑒𝑐𝑘𝑖𝑛𝑔:
1
𝑥
= 8 −
3
𝑥
1
𝑥
+
3
𝑥
= 8
𝑥
4
𝑥
= 8 𝑥
4 = 8𝑥
4
8
=
8𝑥
8
𝑥 =
1
2
1
𝑥
= 8 −
3
𝑥
1
1
2
= 8 −
3
1
2
(
1
1
)(
2
1
) = 8 − (
3
1
)(
2
1
)
2 = 2

17. Thank you for
listening!