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AF1.1 Write and solve one-step linear equations in one variable.

California Standards. AF1.1 Write and solve one-step linear equations in one variable. Also covered: NS2.1, NS2.2, NS2.4.

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AF1.1 Write and solve one-step linear equations in one variable.

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  1. California Standards AF1.1 Write and solve one-step linear equations in one variable. Also covered:NS2.1, NS2.2, NS2.4

  2. The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—toget the variable by itself on one side of the equation.

  3. 3 7 5 7 x – = 3 7 Since is subtracted from x, 3 7 5 7 3 7 3 7 + x – = + 3 7 add to both sides. 1 7 8 7 = x = 1 Example 1A: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. 3 7 5 7 x – = Simplify.

  4. 5 12 3 8 + = t 3 8 Since is added to t, 5 12 3 8 3 8 3 8 – + – = t 3 8 subtract from both sides. 10 24 9 24 t = – 1 24 t = Example 1B: Solving Equations by Adding or Subtracting Solve. Write the answer in simplest form. 3 8 5 12 + t = Find a common denominator. Subtract.

  5. 3 8 1 4 x = 3 8 1 4 = = x Example 2A: Solving Equations by Multiplying Solve. Write the answer in simplest form. 3 8 Multiply by the reciprocal of . 2 1 4 8 3 8 3 3 8 x =  Then simplify.  1 2 3 x = Caution! 3 8 3 8 To undo multiplying by , you can divide by 8 3 or multiply by its reciprocal, .

  6. Additional Example 2B: Solving Equations by Multiplying Solve. Write the answer in simplest form. 8 9 4y = 8 9 4y = Multiply by the reciprocal of 4. 2 1 4 8 9 1 4 Then simplify. =  4y  1 2 9 y =

  7. 1 5 3 4 w = 4 Example 3: Physical Science Application The amount of copper in brass is of the total weight. If a sample contains 4ounces of copper, what is the total weight of the sample? 3 4 1 5 Let w represent the total weight of the sample. Write an equation. 4 3 4 3 1 5 3 4 w   = 4 3 4 Multiply by the reciprocal of · 1 5 7 Write 4 as an improper 21 5 4 3 w =  fraction. 1 28 5 3 5 w = or 5 Then simplify. 3 5 The sample weighs 5 ounces.

  8. 3 8 7 8 x – = 3 8 3 8 Since is subtracted from x, add to both sides. 3 8 7 8 3 8 3 8 + x – = + 1 4 10 8 = 1 x = Check It Out! Example 1 Solve. Write the answer in simplest form. 3 8 7 8 = x – Simplify.

  9. Check It Out! Example 2 Solve. Write the answer in simplest form. 6 7 3y = 6 7 3y = Multiply by the reciprocal of 3. 2 1 3 6 7 1 3 y = 3 Then simplify.   1 2 7 y =

  10. 1 3 1 4 w = 5 Check It Out! Example 3 The amount of copper in zinc is of the total weight. If a sample contains 5ounces of copper, what is the total weight of the sample? 1 4 1 3 Let w represent the total weight of the sample. Write an equation. 4 1 1 4 4 1 1 3  w  = 5 1 4 Multiply by the reciprocal of · 1 3 Write 5 as an improper 16 3 4 1  w = fraction. 64 3 1 3 w = or 21 Multiply. 1 3 The sample weighs 21 ounces.

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