Solving Multistep Equations Objective A L G E
Solving Multistep Equations Objective A L G E B R A • Write and solve multistep equations.
Solving Multistep Equations Key Skills A L G E B R A Keep it balanced! Solve 6 n + 17 = 5 + 4 n – 6 n 17 = 5 – 2 n – 5 12 = ÷– 2 – 2 n ÷– 2 Where do we 6 nstart? Subtract from The goalofisthe to get the Does it matter? each side variable on. Seaside one side Like driving equal sign. to of the equal sign and Heights, you could take Subtract 5 from each the numbers on the side Turnpike to the of the equal sign. otherorside. Parkway Route 280 to the Parkway. Either Divide by – 2 way gets you to the Parkway which you need to take to get to n=– 6 Seaside Heights.
Solving Multistep Equations Just watch what happens It doesn’t matter where you start A 6 n + 17 = 5 + 4 n – 5 – 4 n – 17 L G 6 n + 12 = 4 n 2 n + 17 = 5 6 n = – 12 + 4 n E – 6 n – 17 – 4 n – 6 n B – 4 n R 12 = – 2 n 2 n = – 12 A ÷ 2 n=– 6 ÷– 2 n=– 6 ÷ 2 n=– 6
Solving Multistep Equations Do This Together A L G E B R A Keep it balanced! Solve 3 x + 19 = 4 + 8 x – 3 x 19 = 4 + 5 x – 4 15 = ÷ 5 Subtract 3 x from Theside goalofisthe to get the each variable equal sign. on one side of the equal sign and Subtract 4 from each the numbers on the side of the equal sign. other side. Divide by 5 5 x ÷ 5 x=3
Solving Multistep Equations Just watch the NOT mess up A L G E B R A 3 x + 19 = 4 + 8 x – 3 x 19 = 4 + 5 x – 19 0 = – 15 + 5 x – 5 x = – 15 ÷– 5 x=3
Solving Multistep Equations Try This A L G E B R A Keep it balanced! Solve – 3 x – 9 = – 13 – 7 x + 3 x – 9 = – 13 – 4 x + 13 Add 3 x to each side to get the of. The the goal equalissign. variable on one side of the equal sign and Add 13 to each side the numbers on the of the equal sign. other side. Divide by – 4 4 = – 4 x ÷– 4 x=– 1
Solving Multistep Equations Combining Like Terms First… A L G E B R A Write the original equation. Combine like terms. Add 8 to each side. 4 4 Simplify. Divide each side by 4. Simplify. CHECK
Solving Multistep Equations Using the Distributive Property… A L G E B R A Write the original equation. Distribute the 3. Combine like terms. Subtract from both sides. Simplify Divide both sides. Simplify. CHECK
Solving Multistep Equations Distributing a Negative… A L G E B R A Write the original equation. Distribute the 3 and the negative. Combine like terms. Subtract from both sides. Simplify CHECK
Solving Multistep Equations Multiplying by a Reciprocal First… A L G E B R A
Solving Multistep Equations Practice… A L G E B R A
Solving Multistep Equations A L G E B R A
Solving Multistep Equations Do this together A L G E B R A Mr. Esker has to buy pencils for his company. Supplier A charges $4 per box and $3 for shipping. Supplier B charges $3 per box and $6 for shipping. a. Write equations for both suppliers. b. How many boxes would he need to buy for both companies to charge the same amount?
Solving Multistep Equations Do this together Mr. Esker has to buy pencils for his company. Supplier A charges $4 per box and $3 for shipping. Supplier B charges $3 per box and $6 for shipping. A L G E To write the equation for Supplier A, the C = $3 + 4 b B Cost (what you end up paying) is equal to R the shipping cost (fixed amount, the A constant where the cost starts) + the cost per box multiplied by how boxes are purchased. Try writing the equation for Supplier B. C = $6 + 3 b
Solving Multistep Equations Do this together A L G E B R A In order to find when the 2 Suppliers charge the same amount, set the 2 equations equal to each other. C = 4 b + 3 C = 3 b + 6 4 b + 3 = 3 b + 6 Now Solve for b.
Solving Multistep Equations Do this together A L G E B R A Solve 4 b + 3 = 3 b + 6 – 4 b 3=–b+6 – 6 Subtract 4 b from Theside goalofisthe to get the each variable equal sign. on one side of the equal and Subtract 6 fromsign each the numbers on the side of the equal sign. other side. Divide by – 1 – 3=–b ÷– 1 3=b
Solving Multistep Equations Try This A L G E B R A A car leaves Newark airport and travels at a constant rate of 65 mph to Los Angeles. The car travels through Pittsburgh, which is 370 miles from Newark, and through Las Vegas, which is 2500 miles from Newark. When the car gets to Las Vegas, an airplane leaves Pittsburgh and travels at a constant rate of 550 mph to LA. It travels over Las Vegas as well. When will the airplane fly over the car?
Solving Multistep Equations Try This Let d equal the distance traveled and h equal the elapsed time, the distances must be equal. The important facts are the speeds and how far each vehicle is from Newark when the plane takes off. A L G Car d = 65 h + 2500 E Airplane d = 550 h + 370 B R A 550 h + 370 = 65 h + 2500
Solving Multistep Equations Try This A L G E B R A 550 h + 370 = 65 h + 2500 – 370 550 h = 65 h + 2130 – 65 h 485 h = 2130 ÷ 485 h = 4. 4 hours or 4 hours 24 minutes
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