Objective Solve equations in one variable that contain more than one operation.

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Objective Solve equations in one variable that contain more than one operation.

Example 1A: Solving Two-Step Equations Solve 18 = 4a + 10. 18 = 4a + 10 First a is multiplied by 4. Then 10 is added. Work backward: Subtract 10 from both sides. –10 – 10 8 = 4a Since a is multiplied by 4, divide both sides by 4 to undo the multiplication. 8 = 4a 4 2 = a

Example 1B: Solving Two-Step Equations Solve 5t – 2 = –32. 5t – 2 = –32 First t is multiplied by 5. Then 2 is subtracted. Work backward: Add 2 to both sides. + 2 + 2 5t = –30 Since t is multiplied by 5, divide both sides by 5 to undo the multiplication. 5t = –30 5 t = –6

Check it Out! Example 1a Solve –4 + 7x = 3. –4 + 7x = 3 First x is multiplied by 7. Then –4 is added. Work backward: Add 4 to both sides. + 4 + 4 7x = 7 Since x is multiplied by 7, divide both sides by 7 to undo the multiplication. 7x = 7 7 x = 1

Check it Out! Example 1c Solve . First n is divided by 7. Then 2 is added. Work backward: Subtract 2 from both sides. –2 –2 Since n is divided by 7, multiply both sides by 7 to undo the division. n = 0

Example 2B Continued Solve . Method 2 Multiply by the LCD to clear the fractions. Multiply both sides by 12, the LCD of the fractions. Distribute 12 on the left side. 8r + 9 = 7 Simplify. Since 9 is added to 8r, subtract 9 from both sides to undo the addition. –9 –9 8r = –2

Example 2B Continued Solve . Method 2 Multiply by the LCD to clear the fractions. 8r = –2 Since r is multiplied by 8, divide both sides by 8 to undo the multiplication. 8 8

Method 2 Multiply by the LCD to clear the fractions. Check It Out! Example 2a Solve . Method 2 Multiply by the LCD to clear the fractions. Multiply both sides by 10, the LCD of the fractions. Distribute 10 on the left side. 4x – 5 = 50 Simplify. + 5 + 5 Since 5 is subtracted from 4x, add 5 to both sides to undo the subtraction. 4x = 55

Check It Out! Example 2a Solve . Method 2 Multiply by the LCD to clear the fractions. 4x = 55 Simplify. Since 4 is multiplied by x, divide both sides by 4 to undo the multiplication. 4 4

Method 2 Multiply by the LCD to clear the fractions. Check It Out! Example 2b Solve . Method 2 Multiply by the LCD to clear the fractions. Multiply both sides by 8, the LCD of the fractions. Distribute 8 on the left side. 6u + 4 = 7 Simplify.  4  4 Since 4 is added to 6u, subtract 4 from both sides to undo the addition. 6u = 3

Check It Out! Example 2b Continued Solve . Method 2 Multiply by the LCD to clear the fractions. Since u is multiplied by 6, divide both sides by 6 to undo the multiplication. 6u = 3 6 6