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Learn to solve equations involving decimals.

Learn to solve equations involving decimals. You can solve equations with decimals using inverse operations just as you solved equations with whole numbers. $45.20 + m = $69.95. –$45.20. –$45.20. m = $24.75. Remember!.

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Learn to solve equations involving decimals.

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  1. Learn to solve equations involving decimals.

  2. You can solve equations with decimals using inverse operations just as you solved equations with whole numbers. $45.20 + m = $69.95 –$45.20 –$45.20 m = $24.75

  3. Remember! Use inverse operations to get the variable alone on one side of the equation.

  4. ? 15.7 – 6.2 = 9.5 ? 9.5 = 9.5 Additional Example 1A: Solving One-Step Equations with Decimals Solve the equation. Check your answer. k – 6.2 = 9.5 6.2 is subtracted from k. k – 6.2 = 9.5 + 6.2 + 6.2 Add 6.2 to both sides to undo the subtraction. k = 15.7 Check k – 6.2 = 9.5 Substitute 15.7 for k in the equation. 15.7 is the solution. 

  5. 6 6 ? 6(1.2) = 7.2 ? 7.2 = 7.2 Additional Example 1B: Solving One-Step Equations with Decimals Solve the equation. Check your answer. 6k = 7.2 k is multiplied by 6. 6k = 7.2 Divide both sides by 6 to undo the multiplication. 6k = 7.2 k = 1.2 Check 6k = 7.2 Substitute 1.2 for k in the equation. 1.2 is the solution. 

  6. m 7 m = 0.6 7 4.2 ? = 0.6 7 ? 0.6 = 0.6 Additional Example 1C: Solving One-Step Equations with Decimals Solve the equation. Check your answer. m = 0.6 m is divided by 7. 7 · 7 Multiply both sides by 7 to undo the division. = 0.6 · 7 m = 4.2 Check Substitute 4.2 for m in the equation.  4.2 is the solution.

  7. ? 12.3 – 3.7 = 8.6 ? 8.6 = 8.6 Check It Out: Example 1A Solve the equation. Check your answer. n – 3.7 = 8.6 3.7 is subtracted from n. n – 3.7 = 8.6 + 3.7 + 3.7 Add 3.7 to both sides to undo the subtraction. n = 12.3 Check n – 3.7 = 8.6 Substitute 12.3 for n in the equation. 12.3 is the solution. 

  8. 7 7 ? 7(1.2) = 8.4 ? 8.4 = 8.4 Check It Out: Example 1B Solve the equation. Check your answer. 7h = 8.4 h is multiplied by 7. 7h = 8.4 Divide both sides by 7 to undo the multiplication. 7h = 8.4 h = 1.2 Check 7h = 8.4 Substitute 1.2 for h in the equation. 1.2 is the solution. 

  9. w 9 w = 0.3 9 2.7 ? = 0.3 9 ? 0.3 = 0.3 Check It Out: Example 1C Solve the equation. Check your answer. w = 0.3 w is divided by 9. 9 · 9 Multiply both sides by 9 to undo the division. = 0.3 · 9 w = 2.7 Check Substitute 2.7 for w in the equation.  2.7 is the solution.

  10. Remember! The area of a rectangle is its length times its width. A = lw w l

  11. Additional Example 2A: Measurement Application The area of Emily’s floor is 33.75 m2. If its length is 4.5 meters, what is its width? area = length · width 33.75 = 4.5 · w Write the equation for the problem. Let w be the width of the room. 33.75 = 4.5w 33.75 = 4.5w Divide both sides by 4.5 to undo the multiplication. 4.5 4.5 7.5 = w The width of Emily’s floor is 7.5 meters.

  12. Additional Example 2B: Measurement Application If carpet costs $23 per square meter, what is the total cost to carpet the floor? total cost = area · cost of carpet per square meter Let C be the total cost. Write the equation for the problem. C = 33.75 · 23 C = 776.25 Multiply. The cost of carpeting the floor is $776.25.

  13. Check It Out: Example 2A The area of Yvonne’s bedroom is 181.25 ft2. If its length is 12.5 feet, what is its width? area = length · width 181.25 = 12.5 · w Write the equation for the problem. Let w be the width of the room. 181.25 = 12.5w 181.25 = 12.5w Divide both sides by 12.5 to undo the multiplication. 12.5 12.5 14.5 = w The width of Yvonne’s bedroom is 14.5 feet.

  14. Check It Out: Example 2B If carpet costs $4 per square foot, what is the total cost to carpet the bedroom? total cost = area · cost of carpet per square foot Let C be the total cost. Write the equation for the problem. C = 181.25 · 4 C = 725 Multiply. The cost of carpeting the bedroom is $725.

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