Thursday, Sept. 8 AGENDA: New seat assignments Return/Review Test #1 ∎ AGENDA: New seat assignments Return/Review Test #1 Continue with 7.1

Thursday, Sept. 8 Please get out your NOTEBOOK ∎ Please get out your NOTEBOOK Go to yesterday’s notes on 7.1 ON-LINE MATH BOOK my.hrw.com u/n: google I.D. p/w: lunch number I.D.

∎ 𝑩𝒐𝒐𝒌 𝒑𝒂𝒈𝒆 𝟏𝟗𝟗 Essential Question: How do you solve equations with a variable on both sides of the equal sign?

Need to know: ∎ Variable: a letter that takes the place of an unknown number – Value can change 𝒆𝒙𝒂𝒎𝒑𝒍𝒆: 𝟑𝒙+𝟓=𝟏𝟕 𝒙 is the variable Coefficient: the number IN FRONT of a variable – Shows multiplication 𝒆𝒙𝒂𝒎𝒑𝒍𝒆: 𝟑𝒙+𝟓=𝟏𝟕 𝟑 is the coefficient Constant: a number that stands by itself without an attached variable – value doesn’t change 𝒆𝒙𝒂𝒎𝒑𝒍𝒆: 𝟑𝒙+𝟓=𝟏𝟕 𝟓 is the constant

Need to know (continued): ∎ Isolate the variable – get the 𝒙 by itself A number plus its OPPOSITE =𝟎 𝒆𝒙𝒂𝒎𝒑𝒍𝒆: 𝟑+(−𝟑)=𝟎 A number divided by itself =𝟏 𝒆𝒙𝒂𝒎𝒑𝒍𝒆: 𝟑 𝟑 =𝟏

The goal is to end up with 𝒙=𝒂 𝒏𝒖𝒎𝒃𝒆𝒓 ∎ Looks like: 𝟓𝒙+𝟐=𝟑𝒙+𝟏𝟎 𝒙+𝟐=𝟑𝒙+𝟏𝟎 Notice there is an 𝒙 on BOTH sides of the equal sign The goal is to end up with 𝒙=𝒂 𝒏𝒖𝒎𝒃𝒆𝒓 This is done with 3 steps:

STEPS TO SOLVE EQUATION ∎ STEPS TO SOLVE EQUATION Step 1: Move all of the variables (𝒙) to the LEFT side of = sign You do this by ADDING THE OPPOSITE of what you are trying to move or get rid of

STEPS TO SOLVE EQUATION ∎ STEPS TO SOLVE EQUATION Step 2: Move all of the constants (numbers) to the RIGHT side of = sign Again, you do this by ADDING THE OPPOSITE of what you are trying to move or get rid of

STEPS TO SOLVE EQUATION ∎ STEPS TO SOLVE EQUATION Step 3: Isolate the variable by DIVIDING BOTH SIDES by the COEFFICIENT (the number in front of the variable)

FIRST Review how to solve a two-step equation ∎ FIRST Review how to solve a two-step equation 𝟐𝒙+𝟐= 𝟏𝟎 + −𝟐 −𝟐 𝟐𝒙=𝟖 𝟐 𝟐 𝒙=𝟒

∎ Example #1 Solve for 𝒙: 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 It’s pretty difficult to find the value of 𝒙 without writing all of the steps……not impossible, just difficult. Wanna try? Yes???? No???? It’s actually easier to solve this with algebra than to trying to do it in your head.

Example #1 Solve for 𝒙: 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 ∎ Step 1: Move all of the 𝒙’s to the LEFT side 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 + −𝟔𝒙 −𝟔𝒙 Don’t forget to bring this number down 𝟐𝒙+𝟑= 𝟏𝟑

∎ Example #1 Solve for 𝒙: 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 Step 1: Move all of the 𝒙’s to the LEFT side 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 + −𝟔𝒙 −𝟔𝒙 𝟐𝒙+𝟑= 𝟏𝟑 Step 2: Move all of the constants to the right side 𝟐𝒙+𝟑= 𝟏𝟑 + −𝟑 −𝟑 𝟐𝒙= 𝟏𝟎

∎ Example #1 Solve for 𝒙: 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 Step 1: Move all of the 𝒙’s to the LEFT side 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 + −𝟔𝒙 −𝟔𝒙 𝟐𝒙+𝟑= 𝟏𝟑 Step 2: Move all of the constants to the right side 𝟐𝒙+𝟑= 𝟏𝟑 + −𝟑 −𝟑 𝟐𝒙= 𝟏𝟎 Step 3: Isolate the variable (Divide by the coefficient) 𝟐𝒙= 𝟏𝟎 𝟐 𝟐 𝒙=𝟓

∎ Check your answer by plugging 5 into the original equation in place of 𝒙 𝟖𝒙+𝟑=𝟔𝒙+𝟏𝟑 𝟖 𝟓 +𝟑=𝟔(𝟓)+𝟏𝟑 𝟒𝟎+𝟑=𝟑𝟎+𝟏𝟑 𝟒𝟑=𝟒𝟑 The left side equals the right side, so 𝒙=𝟓 is correct Note that this doesn’t mean that 𝒙=𝟒𝟑

𝒙=−𝟓 ∎ Example #2 Solve for 𝒙: −𝟐𝒙−𝟒=𝟐𝒙+𝟏𝟔 −𝟐𝒙−𝟒=𝟐𝒙+𝟏𝟔 + −𝟐𝒙 −𝟐𝒙 Step 1: Move all of the 𝒙’s to the LEFT side −𝟐𝒙−𝟒=𝟐𝒙+𝟏𝟔 + −𝟐𝒙 −𝟐𝒙 −𝟒𝒙−𝟒= 𝟏𝟔 Step 2: Move all of the numbers to the other side + +𝟒 +𝟒 −𝟒𝒙=𝟐𝟎 Step 3: Isolate the variable −𝟒 −𝟒 Check you answer by plugging 4 into the original equation in place of 𝒙 𝒙=−𝟓 −𝟐𝒙−𝟒=𝟐𝒙+𝟏𝟔 −𝟐 −𝟓 −𝟒=𝟐(−𝟓)+𝟏𝟔 𝟏𝟎−𝟒=−𝟏𝟎+𝟏𝟔 𝟔=𝟔

𝒙=𝟐 ∎ Solve for 𝒙: 𝟓𝒙−𝟏=−𝟑𝒙+𝟏𝟓 𝟓𝒙−𝟏=−𝟑𝒙+𝟏𝟓 + 𝟑𝒙 𝟑𝒙 𝟖𝒙−𝟏= 𝟏𝟓 + +𝟏 +𝟏 YOUR TURN Step 1: Move all of the 𝒙’s to the LEFT side 𝟓𝒙−𝟏=−𝟑𝒙+𝟏𝟓 + 𝟑𝒙 𝟑𝒙 𝟖𝒙−𝟏= 𝟏𝟓 Step 2: Move all of the numbers to the other side + +𝟏 +𝟏 𝟖𝒙=𝟏𝟔 Step 3: Isolate the variable 𝟖 𝟖 Check you answer by plugging 4 into the original equation in place of 𝒙 𝒙=𝟐 𝟓𝒙−𝟏=−𝟑𝒙+𝟏𝟓 𝟓 𝟐 −𝟏=−𝟑(𝟐)+𝟏𝟓 𝟏𝟎−𝟏=−𝟔+𝟏𝟓 𝟗=𝟗

∎ Use the next 2-3 minutes to discuss/review the lesson, do additions to your notes, etc.

∎ Solve for 𝒏: 𝟑𝒏−𝟏=𝟐𝒏+𝟓 + −𝟐𝒏 −𝟐𝒏 𝒏−𝟏= 𝟓 + +𝟏 +𝟏 𝒏=𝟔 PRACTICE PROBLEM Solve for 𝒏: 𝟑𝒏−𝟏=𝟐𝒏+𝟓 + −𝟐𝒏 −𝟐𝒏 𝒏−𝟏= 𝟓 + +𝟏 +𝟏 𝒏=𝟔 CHECK: 𝟑(𝟔)−𝟏=𝟐(𝟔)+𝟓 CHECK: 𝟏𝟖−𝟏=𝟏𝟐+𝟓 CHECK: 𝟏𝟕=𝟏𝟕

𝒙=−𝟐 ∎ Solve for 𝒙: −𝟔𝒙−𝟒=𝟑𝒙+𝟏𝟒 + −𝟑𝒙 −𝟑𝒙 −𝟗𝒙−𝟒= 𝟏𝟒 + +𝟒 +𝟒 −𝟗𝒙=𝟏𝟖 PRACTICE PROBLEM + −𝟑𝒙 −𝟑𝒙 −𝟗𝒙−𝟒= 𝟏𝟒 + +𝟒 +𝟒 −𝟗𝒙=𝟏𝟖 −𝟗 −𝟗 𝒙=−𝟐 CHECK −𝟔𝒙−𝟒=𝟑𝒙+𝟏𝟒 CHECK −𝟔(−𝟐)−𝟒=𝟑(−𝟐)+𝟏𝟒 CHECK: 𝟏𝟐−𝟒=−𝟔+𝟏𝟒 CHECK: 𝟖=𝟖

𝒙=𝟕 ∎∎ Solve for 𝒙: 𝒙−𝟑=−𝟐𝒙+𝟏𝟖 + +𝟐𝒙 +𝟐𝒙 𝟑𝒙−𝟑= 𝟏𝟖 + +𝟑 +𝟑 𝟑𝒙=𝟐𝟏 𝟑 𝟑 PRACTICE PROBLEM + +𝟐𝒙 +𝟐𝒙 𝟑𝒙−𝟑= 𝟏𝟖 + +𝟑 +𝟑 𝟑𝒙=𝟐𝟏 𝟑 𝟑 𝒙=𝟕 CHECK 𝒙−𝟑=−𝟐𝒙+𝟏𝟖 CHECK 𝟕 −𝟑=−𝟐(𝟕)+𝟏𝟖 CHECK: 𝟒=−𝟏𝟒+𝟏𝟖 CHECK: 𝟒=𝟒