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

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………….

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

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………….

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

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………….

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

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………….

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