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EXAMPLE 1

= –15. x. x. + 8. + 8. = –15. – 8. – 8. –23. x. =. ANSWER. The solution is –23. Solving an Equation Using Subtraction. EXAMPLE 1. Original equation. Subtract 8 from each side to undo addition. Simplify. x is by itself. ?. 13. 17.5 – 4.5. =. 13 = 13 ✓.

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EXAMPLE 1

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  1. = –15 x x + 8 + 8 = –15 –8 – 8 –23 x = ANSWER The solution is –23. Solving an Equation Using Subtraction EXAMPLE 1 Original equation Subtract 8 from each side to undo addition. Simplify. xis by itself.

  2. ? 13 17.5–4.5 = 13= 13 ✓ Solving an Equation Using Addition EXAMPLE 2 c–4.5 = 13 c–4.5 = 13 Original equation c–4.5+ 4.5= 13+ 4.5 Add 4.5 to each side to undo subtraction. c= 17.5 Simplify. cis by itself. Check Substitute 17.5 for c in original equation.

  3. A cliff has a height of about 1500 feet. If you have already climbed 675 feet, how much farther do you have to climb to reach the top? Using a Model EXAMPLE 3 Rock Climbing SOLUTION Use the diagram to help you write an algebraic model. Let xrepresent the distance left to climb.

  4. ANSWER You have about 825 feet left to climb. Using a Model EXAMPLE 3 1500= x + 675 Write an algebraic model. 1500–675= x + 675–675 Subtract 675 from each side. 825= x Simplify. xis by itself.

  5. ? 13 11+ 9 = 11= 11 ✓ for Examples 1, 2, and 3 GUIDED PRACTICE Solve the equation. Check your solution. 1.x + 9 = 20 x+9 = 20 Original equation c+9– 9= 20– 9 Subtract 9 from each side. x= 11 Simplify. xis by itself. Check Substitute 11 for x in original equation.

  6. ? 3 – 13 –10 = –10= –10 ✓ for Examples 1, 2, and 3 GUIDED PRACTICE 2.–10= 3+ y –10= 3 +y Original equation –10 – 3 = 3 +y– 3 Subtract 3 from each side. –13 = y Simplify. yis by itself. Substitute –13 for y Check in original equation.

  7. ? –15 –1 –14 = –1= –1 ✓ for Examples 1, 2, and 3 GUIDED PRACTICE 3.m –14= –15 m–14= –15 Original equation m–14 + 14= –15+14 Add 14 from each side. m= –1 Simplify. mis by itself. Check Substitute –1 for m in original equation.

  8. ? 8.4 – 6.4 2 = 2= 2✓ for Examples 1, 2, and 3 GUIDED PRACTICE 4.2= z–6.4 2 = z –6.4 Original equation 2 + 6.4 = z – 6.4 +6.4 Subtract 6.4 from each side. 8.4 = z Simplify. zis by itself. Substitute 8.4 for z Check in original equation.

  9. Jerry had 113 seashells before their collections were combined ANSWER for Examples 1, 2, and 3 GUIDED PRACTICE 5.Seashells Lucinda combines her 49 seashells with Jerry’s seashells, for a total of 162. Write and solve an addition equation to find how many seashellsJerry had before their collections were combined. SOLUTION Let s represent Jerry’s seashells s + 49 = 162 Write an algebraic model. s + 49 –49= 162–49 Subtract 49 from each side. s= 113 Simplify. sis by itself.

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