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More Two-Step Equations

More Two-Step Equations. Practice 4-5. Let g =the price of gas; 6g-20 Let d =the distance from Boston to New York; ½ d-25 Let e =the number of eggs needed in the recipe; 5e-2 Let m =the number of megabytes in a computer; m-10/6 H=3 S=9 Y=1 G=4 J=2 W=4 H=6 G=32 B=7 $5+$2m; $45.

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More Two-Step Equations

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  1. More Two-Step Equations

  2. Practice 4-5 • Let g=the price of gas; 6g-20 • Let d=the distance from Boston to New York; ½ d-25 • Let e=the number of eggs needed in the recipe; 5e-2 • Let m=the number of megabytes in a computer; m-10/6 • H=3 • S=9 • Y=1 • G=4 • J=2 • W=4 • H=6 • G=32 • B=7 • $5+$2m; $45

  3. Guided Problem Solving 4-5 • 2 zucchini per minute; 30 sliced zucchini; already sliced 12 zucchini • Find how long it will take to finish slicing the zucchini • The number of minutes it will take to finish slicing the zucchini • 30 • 12 • 30-12=18 • 2 minutes • 2t=18 • 9 minutes • 9x2=18; yes • T=2 hours

  4. Solving 2 Step Equations When you do something to one side of an equation,

  5. Solving 2 Step Equations you have to do exactly the same thing to the other side.

  6. Solving 2 Step Equations To solve an equation means to find every number that makes the equation true.

  7. Solving 2 Step Equations In the equation, x is the number you add to 7 to get 15.

  8. Solving 2 Step Equations What is the number? 8, of course. So we would write thesolution x = 8

  9. Solving 2 Step Equations In some equations, the solution is obvious.

  10. Solving 2 Step Equations But in other equations, the solution is not so obvious.

  11. Solving 2 Step Equations Many times we need a way to solve equations. Especially if there is more than one step to solve.

  12. SADMEP 1) Undo the addition or subtraction operation first, by using inverse operations. 2) Undo the multiplication or divisionoperationsecond, by using inverse operations.

  13. Solving 2 Step Equations REMEMBER

  14. Solving 2 Step Equations To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations. Inverse Operations are like Opposites.

  15. Solving 2 Step Equations I am going to show you 2 ways to solve this equation. 3x + 4 = 16 Hard way Easy way Undo Multiplication or Division 1st Undo Addition or Subtraction 1st

  16. Solving 2 Step Equations Hard way Easy way Undo Multiplication or Division 1st Undo Addition or Subtraction 1st 3x + 4 = 16 3x + 4 = 16 3 3 -4 -4 3x 4 16 = + 3x = 12 3 3 3 3 3 4 16 x = + x = 4 3 3 4 4 - - 3 3 12 x = 3 x 4 =

  17. Solving 2 Step Equations 1)GOAL: Get the variable on one side of the equation. 2) You always perform the same operation to both sides of an equation. 3) To undo an operation you perform its opposite operation to both sides of the equation. 4) It is easier if you undo addition or subtraction before you undo multiplication or division.

  18. Solving 2 Step Equations Get the variable alone. - 4 - 4 Subtract 4 from both sides. 2x + 4 = 10 2x = 6 __ __ 2 2 +4 and -4 cancel out Divide both sides by 2 x = 3 2 divided by 2 cancel to 1 2(3) +4 = 10 Show your check. 6 + 4 = 10 10 = 10 Finish your check.

  19. Solving 2 Step Equations Get the variable alone. + 10 +10 Add 10 to both sides. 3m - 10 = 17 3m = 27 __ __ 3 3 +10 and -10 cancel out Divide both sides by 3 m = 9 3 divided by 3 cancel to 1 3(9) – 10 = 17 Show your check. 27 – 10 = 17 Finish your check. 17 = 17

  20. Solving 2 Step Equations x 3 Get the variable alone. +4 +4 Add 4 to both sides. – 4 = 8 x 3 = 12 + 4 and -4 cancel out. x 3 Multiply both sides by 3. 3 ( ) = 3 12 3 divided by 3 cancel to 1 x = 36 Show your check. 36 3 – 4 = 8 Finish your check. 12 – 4 = 8 8 = 8

  21. Solving 2 Step Equations x 2 Get the variable alone. - 6 - 6 Subtract 6 from both sides. + 6 = 14 x 2 = 8 + 6 and -6 cancel out. x 2 Multiply both sides by 2. 2 ( ) = 2 8 2 divided by 2 cancel to 1 x = 16 16 2 Show your check. + 6 = 14 8 + 6 = 14 Finish your check. 14 = 14

  22. Solving 2 Step Equations What Operation Do You Do? FIRSTSECOND 1) 3x + 8 = 24 Divide by 3 Subtract 8 2) 5x - 10 = 19 Divide by 5 Add 10 3) x - 4 = 20 2 Add 4 Multiply by 2 4) - 30 = -5x + 5 Divide by -5 Subtract 5

  23. Solving 2 Step Equations

  24. Solving 2 Step Equations

  25. Solving 2 Step Equations Think about what you need to do to isolate the variable. Get rid of addition or subtraction first. Second get rid of multiplication or division.

  26. Solving 2 Step Equations The End!

  27. #12 2 Step Subtract/Multiply Equation Get the variable alone. +10 +10 Add 10 to both sides. • 3m - 10 = 17 __ __ 3 3 3m = 27 +10 and -10 cancel out Divide both sides by 3 m = 9 3 divided by 3 cancel to 1 3(9) – 10 =17 Show your check. 27 – 10 =17 Finish your check. 17 =17

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