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Transcript
```Notes1.1
SolvingEquations
Anequationisamathematicalsentencethat
usestheequalsign(=)toshowtwo
expressionsthatareequivalent.
3𝑥 + 2 = 8 5𝑥 − 1 = 4𝑥 + 2
Tosolveanequation,youneedtouseinverse
(opposite)operationstoisolatethe
variable—getthexbyitself:
𝑥 + 2 = 12 𝑥 + 2 − 2 = 12 − 2
𝑥 = 10
Thesearetheinverseoperationsthatyou
needtoknow…
subtraction.
𝑥+8
= 14 𝑥 + 8 − 8 = 14 − 8
𝑥 = 6
Theinverseoperationofmultiplicationis
division.
2𝑥
!
!
2𝑥 ∙ ! = 12 ∙ ! !!
!
!!
!
= 12 =
=
!"
!
!∙!
!
𝑥 = 6
Examples:
5𝑥 − 10 = 20
!
𝑥
+
9
=
21
!
Yousolve:
10 = 2𝑥 + 1
4𝑦 + 3 = 5
NOTE:inanequationwithmultiple
fractions,tryclearingthembymultiplying
allofthetermsbytheLeastCommon
Denominator
1
1
5
𝑦+ = 3
4 12
12 1
1 12
5 12
𝑦+
=
1 3
4 1
12 1
12
12 60
𝑦+
= 3
4
12
4𝑦 + 3 = 5
4𝑦 + 3 − 3 = 5 − 3
4𝑦 = 2 1
1
4𝑦 =
2
4
4
4
2
𝑦= 4
4
1
𝑦= 2
```
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