Unit 3. Day 12.

6th Grade Solving: 7th Grade Solving: 8th Grade Solving: One-step Equations Equations of the form x + p = q  and  px = q  where  p, q and x are all nonnegative rational numbers. 7th Grade Solving: Two/three-step Equations Equations of the form  px + q = r  and  p(x + q) = r where p, q, and r are specific rational numbers. 8th Grade Solving: Three/four/five-step Equations Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

𝑺𝒕𝒆𝒑𝒔 𝒕𝒐 𝒔𝒐𝒍𝒗𝒆 𝒂𝒏𝒚 𝒆𝒒𝒖𝒂𝒕𝒊𝒐𝒏 1) 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 a) Distribute b) Combine Like Terms 2) Move the variable to one side of the equation 3) Inverse Operations (Homeless man & wife) Step 1 Step 2 Step 3 Step 4 Step 5

= = = 5(𝑥 + 2) –3𝑥 + 4 = −2𝑥 + 30 5𝑥 + 10 –3𝑥 + 4 = −2𝑥 + 30 2𝑥 + 14 Example A: Solve. 5(𝑥 + 2) –3𝑥 + 4 = −2𝑥 + 30 5𝑥 + 10 –3𝑥 + 4 = −2𝑥 + 30 = 2𝑥 + 14 −2𝑥 + 30 +2𝑥 +2𝑥 = 4𝑥 + 14 30 −14 −14 = 4𝑥 16 4 4 𝑥 = 4

= = = 2 𝑦−4 +4𝑦−5 =3𝑦 +2 2𝑦 −8 +4𝑦−5 =3𝑦+2 6𝑦 −13 3𝑦+2 −3𝑦 −3𝑦 3𝑦 −13 Example B*: Solve. 2 𝑦−4 +4𝑦−5 =3𝑦 +2 2𝑦 −8 +4𝑦−5 =3𝑦+2 = 6𝑦 −13 3𝑦+2 −3𝑦 −3𝑦 = 3𝑦 −13 2 +13 +13 = 3𝑦 15 3 3 𝑦 =5

= = = 9− 2𝑥−3 –3𝑥 + 4 = −4𝑥+20+𝑥 9 –3𝑥 + 4 =−4𝑥 +20+𝑥 −2𝑥 +3 16 −5𝑥 Example C*: Solve. 9− 2𝑥−3 –3𝑥 + 4 = −4𝑥+20+𝑥 9 –3𝑥 + 4 =−4𝑥 +20+𝑥 −2𝑥 +3 16 = −5𝑥 −3𝑥 +20 +3𝑥 +3𝑥 = 16 −2𝑥 20 −16 −16 = −2𝑥 4 −2 −2 𝑥 =−2

= = = = − 2𝑚 − 9 − 𝑚 − 11 +𝑚 +𝑚 −𝑚 −9 − 11 + 9 +9 −𝑚 −2 −1 −1 𝑚=2 Example D*: BIG MAMA!!! 3𝑚−2 4𝑚+2 −7+𝑚+2 𝑚+1 =3𝑚 −3−2𝑚+4−2(𝑚+6) = 3𝑚 –8𝑚 −4 −7+𝑚 +2𝑚 +2 3𝑚−3−2𝑚+4 −2𝑚 −12 = − 2𝑚 − 9 − 𝑚 − 11 +𝑚 +𝑚 = −𝑚 −9 − 11 + 9 +9 = −𝑚 −2 −1 −1 𝑚=2

= = 2 𝑎−4 +4𝑎−5 =6𝑎 +2 −13 −13 2𝑎 −8 +4𝑎−5 =6𝑎+2 −13 6𝑎 −13 6𝑎+2 −13 Example E*: Solve. 2 𝑎−4 +4𝑎−5 =6𝑎 +2 −13 −13 2𝑎 −8 +4𝑎−5 =6𝑎+2 −13 = 6𝑎 −13 6𝑎+2 −13 −6𝑎 −6𝑎 = −13 2 𝑁𝑜 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛 𝐼𝑛𝑓𝑖𝑛𝑖𝑡𝑒 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛

Example F: Write an equation and solve. A mountain climber wants to cut a rope 213 feet long into three pieces. If each piece is to be 2 feet longer than the previous one, where should he make the cuts? 𝑥 𝑥+2 𝑥+4 𝑥+𝑥+2+𝑥+4=213 =213 3𝑥 + 6 −6 −6 69, 71, 73 ft. 3𝑥 = 207 3 3 𝑥 = 207 3 = 69

Example G: Write an equation and solve. Mr. Jordan wants to build a dog run. If he has 28 meters of fencing and the fence is to be 6 meters longer than it is wide, find its dimensions. 𝑤+6 𝑙 𝑤 𝑤 4 𝑚 × 10 𝑚 𝑤+6 𝑙 𝑃=𝑤+𝑤+𝑙+𝑙 𝑃=2 𝑤+𝑙 𝑃 𝑤+𝑤+ + 28=2 𝑤+ 28= 28 = 𝑤+6 𝑙 𝑤+6 𝑙 𝑤+6 28= 28=2 2𝑤+6 4𝑤 + 12 −12 −12 4𝑤 + 12 −12 −12 16 = 4𝑤 16 = 4𝑤 4 4 4 4 4 = 𝑤 4 = 𝑤