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Page 𝟐𝟎𝟓
Essential Question: How do you solve equations that contain fractions & decimals

2. 𝟒 𝟒 Solving Equations With Fractions 𝟏 𝟐 𝒙+𝟒= 𝟑 𝟒 𝒙−𝟒 𝟏 𝟐 𝒙+𝟒= 𝟑 𝟒 𝒙−𝟒∎
Solving Equations With Fractions
𝟏 𝟐 𝒙+𝟒= 𝟑 𝟒 𝒙−𝟒
𝟏 𝟐 𝒙+𝟒= 𝟑 𝟒 𝒙−𝟒 𝟒
Step 1: FIND THE LOWEST
COMMON DENOMINATOR
Step 2: MULTIPLY ALL TERMS BY THE
LOWEST COMMON DENOMINATOR 𝟒 𝟐
𝟒 𝟏 ∙
𝟏 𝟐 𝒙+𝟒 = 𝟑 𝟒 𝒙−𝟒
𝟒 𝟏 ∙
Step 3: CANCEL ALL FRACTIONS ∙𝟒 ∙𝟒
Step 4: MULTIPLY 𝟐𝒙
+𝟏𝟔
=𝟑𝒙
−𝟏𝟔
Continue………….

3. 𝒙 =−𝟏𝟖 𝟐𝒙+𝟏𝟓=𝟏𝒙−𝟑 + −𝟏𝒙 −𝟏𝒙 𝟏𝒙+𝟏𝟓 = −𝟑 + −𝟏𝟓 −𝟏𝟓 𝟏𝒙 = −𝟏𝟖 ∎
Step 5…….stuff you know how to do:
𝟐𝒙+𝟏𝟓=𝟏𝒙−𝟑
+ −𝟏𝒙 −𝟏𝒙
𝟏𝒙+𝟏𝟓 = −𝟑
+ −𝟏𝟓 −𝟏𝟓
𝟏𝒙 = −𝟏𝟖
𝒙 =−𝟏𝟖

4. 𝟑 𝟑 Solving Equations With Fractions 𝟐 𝟑 𝒙+𝟓= 𝟏 𝟑 𝒙−𝟏 𝟐 𝟑 𝒙+𝟓= 𝟏 𝟑 𝒙−𝟏∎
Solving Equations With Fractions
𝟐 𝟑 𝒙+𝟓= 𝟏 𝟑 𝒙−𝟏
𝟐 𝟑 𝒙+𝟓= 𝟏 𝟑 𝒙−𝟏 𝟑
Step 1: FIND THE LOWEST
COMMON DENOMINATOR
Step 2: MULTIPLY ALL TERMS BY THE
LOWEST COMMON DENOMINATOR 𝟑
𝟑 𝟏 ∙
𝟐 𝟑 𝒙+𝟓 = 𝟏 𝟑 𝒙−𝟏
𝟑 𝟏 ∙
Step 3: CANCEL ALL FRACTIONS ∙𝟑 ∙𝟑
Step 4: MULTIPLY 𝟐𝒙
+𝟏𝟓
=𝟏𝒙 −𝟑
Continue………….

5. 𝒙 = 𝟑𝟐 𝟐𝒙+𝟏𝟔=𝟑𝒙−𝟏𝟔 + −𝟑𝒙 −𝟑𝒙 −𝟏𝒙+𝟏𝟔 = −𝟏𝟔 + −𝟏𝟔 −𝟏𝟔 −𝟏𝒙 = −𝟑𝟐 −𝟏 −𝟏 ∎
Step 5…….stuff you know how to do:
𝟐𝒙+𝟏𝟔=𝟑𝒙−𝟏𝟔
+ −𝟑𝒙 −𝟑𝒙
−𝟏𝒙+𝟏𝟔 = −𝟏𝟔
+ −𝟏𝟔 −𝟏𝟔
−𝟏𝒙 = −𝟑𝟐
−𝟏 −𝟏
𝒙 = 𝟑𝟐

6. 𝟕 𝟕 Solving Equations With Fractions 𝟏 𝟕 𝒙−𝟔= 𝟑 𝟕 𝒙−𝟒 𝟏 𝟕 𝒙−𝟔= 𝟑 𝟕 𝒙+𝟒∎
Solving Equations With Fractions
𝟏 𝟕 𝒙−𝟔= 𝟑 𝟕 𝒙−𝟒
𝟏 𝟕 𝒙−𝟔= 𝟑 𝟕 𝒙+𝟒 𝟕
Step 1: FIND THE LOWEST
COMMON DENOMINATOR
Step 2: MULTIPLY ALL TERMS BY THE
LOWEST COMMON DENOMINATOR 𝟕
𝟕 𝟏 ∙
𝟏 𝟕 𝒙−𝟔 = 𝟑 𝟕 𝒙+𝟒
𝟕 𝟏 ∙
Step 3: CANCEL ALL FRACTIONS ∙𝟕 ∙𝟕
Step 4: MULTIPLY 𝟏𝒙
−𝟒𝟐
=𝟑𝒙
+𝟐𝟖
Continue………….

7. 𝒙 =−𝟑𝟓 𝟏𝒙−𝟒𝟐=𝟑𝒙+𝟐𝟖 + −𝟑𝒙 −𝟑𝒙 −𝟐𝒙−𝟒𝟐 = 𝟐𝟖 + +𝟒𝟐 +𝟒𝟐 −𝟐𝒙 = 𝟕𝟎 −𝟐 −𝟐 ∎
Step 5…….stuff you know how to do:
𝟏𝒙−𝟒𝟐=𝟑𝒙+𝟐𝟖
+ −𝟑𝒙 −𝟑𝒙
−𝟐𝒙−𝟒𝟐 = 𝟐𝟖
+ +𝟒𝟐 +𝟒𝟐
−𝟐𝒙 = 𝟕𝟎
−𝟐 −𝟐
𝒙 =−𝟑𝟓

8. 𝟏𝟐 𝟏𝟐 Solving Equations With Fractions 𝟓 𝟔 𝒙+𝟏=− 𝟏 𝟐 𝒙+ 𝟏 𝟒∎
Solving Equations With Fractions
𝟓 𝟔 𝒙+𝟏=− 𝟏 𝟐 𝒙+ 𝟏 𝟒
𝟓 𝟔 𝒙+𝟏=− 𝟏 𝟐 𝒙+ 𝟏 𝟒 𝟏𝟐
Step 1: FIND THE LOWEST
COMMON DENOMINATOR
Step 2: MULTIPLY ALL TERMS BY THE
LOWEST COMMON DENOMINATOR 𝟏𝟐
Step 3: CANCEL ALL FRACTIONS 𝟑 𝟔 𝟐
𝟏𝟐 𝟏 ∙
𝟓 𝟔 𝒙+𝟏 = − 𝟏 𝟐 𝒙+ 𝟏 𝟒
𝟏𝟐 𝟏 ∙
∙ 𝟏𝟐 𝟏
∙𝟏𝟐
𝟏𝟎𝒙
+𝟏𝟐
=−𝟔𝒙
+ 𝟑
Step 4: MULTIPLY
Continue………….

9. 𝒙 = 𝟗 𝟏𝟔 𝟏𝟎𝒙+𝟏𝟐=−𝟔𝒙+𝟑 + +𝟔𝒙 +𝟔𝒙 𝟏𝟔𝒙+𝟏𝟐 = 𝟑 + −𝟏𝟐 −𝟏𝟐 𝟏𝟔𝒙 = 𝟗 𝟏𝟔 𝟏𝟔 ∎∎
Step 5…….stuff you know how to do:
𝟏𝟎𝒙+𝟏𝟐=−𝟔𝒙+𝟑
+ +𝟔𝒙 𝟔𝒙
𝟏𝟔𝒙+𝟏𝟐 = 𝟑
+ −𝟏𝟐 −𝟏𝟐
𝟏𝟔𝒙 = 𝟗
𝟏𝟔 𝟏𝟔
𝒙 = 𝟗 𝟏𝟔