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Preview Warm Up California Standards Lesson Presentation

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**Warm Up in Spiral. Solve. 1. x – 16 = 8 2. 7a = 35 3. x = 24**

4. y + 21 = 31 x = 24 a = 5 x 12 x = 132 = 11 y = 10

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

Also covered: NS2.1, NS2.2, NS2.4 California Standards

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

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**Additional Example 1A: Solving Equations by Adding or Subtracting**

Solve. Write the answer in simplest form. 3 7 5 7 x – = Think: What is happening to x. How do I undo that? x – 3 7 = 5 3 7 Since is subtracted from x, add to both sides. x – 3 7 + = 5 x = 8 7 1 Simplify.

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**Additional Example 1B: Solving Equations by Adding or Subtracting**

Solve. Write the answer in simplest form. 3 8 5 12 + t = 3 8 + t = 5 12 Since is added to t, 3 8 subtract from both sides. 3 8 + t – = 5 12 t = 10 24 – 9 Find a common denominator. t = 1 24 Subtract.

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**Additional Example 1C: Solving Equations by Adding or Subtracting**

Solve. Write the answer in simplest form. 4 9 1 2 + r = 4 9 + r 1 2 = Since is added to r, 4 9 subtract from both sides. 4 9 r 4 9 1 2 4 9 + – = – – r = 9 18 8 Find a common denominator. r = 1 18 Subtract.

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**Additional Example 1C Continued**

Check. 4 9 1 2 + r = Substitute for r. 1 18 4 9 + 1 18 1 2 = ? 8 18 + 1 9 = ? Find a common denominator. = 9 18 Add. You can check that a value is a solution to an equation by substituting the value for the variable. Substitute and solve. Is it correct? Helpful Hint

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**Solve. Write the answer in simplest form.**

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

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**+ y = Check It Out! Example 1B**

Solve. Write the answer in simplest form. 1 4 3 8 + y = 1 4 + y = 3 8 Since is added to y, subtract from both sides. 1 4 1 4 3 8 + y – = 3 8 y = – 2 Find a common denominator. y = 1 8 Subtract.

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**Check It Out! Example 1B Continued**

4 3 8 + y = Substitute for y. 1 8 1 4 + 1 8 3 8 = ? 2 8 + 1 3 = ? Find a common denominator. = 3 8 Add.

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**Solve. Write the answer in simplest form.**

Check It Out! Example 1C Solve. Write the answer in simplest form. 3 14 2 7 + t = 3 14 + t = 2 7 Since is added to t, 3 14 subtract from both sides. 3 14 + t – = 2 7 t = – 3 14 4 Find a common denominator. t = 1 14 Subtract.

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**Additional Example 2A: Solving Equations by Multiplying**

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

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**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 1 4 8 9 = Then simplify. 4y 1 2 9 y =

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Check It Out! Example 2A Solve. Write the answer in simplest form. 3 4 1 2 x = 3 4 = 1 2 x 3 4 Multiply by the reciprocal of . 2 3 4 . 4 3 1 2 . 4 3 x = Then simplify. 1 2 3 x =

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

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**Additional Example 3: Physical Science Application**

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

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

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**Solve. Write each answer in simplest form. 1. 2. 3. 4.**

Lesson Quiz Solve. Write each answer in simplest form. 1. 2. 3. 4. 3 8 5 8 x – = 1 7 16 19 32 5 32 y + = x 4 3 7 12 7 5 or 1 = 3 4 1 3 16 9 7 or 1 x = 1 5. Over the course of a week, Marissa ate some apples from a basket on the table. She left 20 apples in the basket. This was five-eighths the number of apples her mother had picked earlier in the week. How many apples did her mother pick? 32

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