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3.2 Solve Two-Step Equations

3.2 Solve Two-Step Equations. Students will solve two-step equations using Algebra. Students will do assigned homework. Students will study vocabulary words. Lets Learn by Video. Lesson 3.2, For use with pages 141-146. Solve the equation. 1. 3 x = –18. –6. ANSWER. 2. b + 21 = 11.

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3.2 Solve Two-Step Equations

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  1. 3.2 Solve Two-Step Equations Students will solve two-step equations using Algebra. Students will do assigned homework. Students will study vocabulary words.

  2. Lets Learn by Video

  3. Lesson 3.2, For use with pages 141-146 Solve the equation. 1. 3x = –18 –6 ANSWER 2. b + 21 = 11 ANSWER –10

  4. Lesson 3.2, For use with pages 141-146 Solve the equation. 3. Simplify the expression 3(x + 2) – 4x + 1. –x + 7 ANSWER 4. There are three times as many goats as sheep in a petting zoo. Find the number of sheep if the total number of goats and sheep is 28. 7sheep ANSWER

  5. Daily Homework Quiz For use after Lesson 3.1 Solve the equation. Check your solution. 1. –6+ a = –2 ANSWER 4 2. 8 = m – 7 ANSWER 15 3. 9k = –72 ANSWER –8

  6. Daily Homework Quiz For use after Lesson 3.1 x 4. 12 = –5 ANSWER –60 Earth orbits the Sun at an average speed of 29.79 kilometers per second. Find how long it takes, to the nearest hundredth of a second, for Earth to travel 500 kilometers. 5. ANSWER 16.78 sec

  7. EXAMPLE 1 Solve a two-step equation x Solve + 5 = 11. 2 x 11 + 5 = Write original equation. 2 x + 5 – 5 = 11 – 5 Subtract 5 from each side. 2 x 6 = Simplify. 2 x 2 = 2 6 Multiply each side by 2. 2 x = 12 Simplify. ANSWER The solution is 12. Check by substituting 12 for x in the original equation.

  8. EXAMPLE 1 Solve a two-step equation x 11 + 5 = CHECK Write original equation. 2 ? 12 11 + 5 = Substitute 12 for x. 2 11 11 = Simplify. Solution checks.

  9. for Example 1 GUIDED PRACTICE Solve the equation. Check your solution. 1. 5x + 9 = 24 ANSWER 3

  10. for Example 1 GUIDED PRACTICE Solve the equation. Check your solution. 2. 4y – 4= 16 ANSWER 5

  11. for Example 1 GUIDED PRACTICE Solve the equation. Check your solution. z 3. –1 = – 7 3 ANSWER 18

  12. EXAMPLE 2 Solve a two-step equation by combining like terms Solve7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. 3x 21 = Divide each side by 3. 3 3 x = 7 Simplify.

  13. EXAMPLE 3 Find an input of a function The output of a function is 3 less than 5 times the input. Find the input when the output is 17. SOLUTION STEP1 Write an equation for the function. Let x be the input and y be the output y = 5x – 3 y is 3 less than 5 times x. STEP 2 Solve the equation for x when y = 17.

  14. EXAMPLE 3 Find an input of a function y = 5x – 3 Write original function. 17 = 5x – 3 Substitute 17 for y. 17 + 3= 5x – 3 +3 Add 3 to each side. 20 = 5x Simplify. 20 5x Divide each side by 5. = 5 5 4 = x Simplify. ANSWER An input of 4 produces an output of 17.

  15. EXAMPLE 3 Find an input of a function CHECK y = 5x– 3 Write original function. ? 17 = 5(4) – 3 Substitute 17 for y and 4 for x. ? 17 = 20– 3 Multiply 5 and 4. Simplify. Solution checks. 17 = 17

  16. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Check your solution. 4. 4w + 2w = 24 ANSWER 4

  17. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Check your solution. 5. 8t – 3t = 35 ANSWER 7

  18. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Check your solution. 6. –16= 5d – 9d ANSWER 4

  19. for Examples 2 and 3 GUIDED PRACTICE 7. The output of a function is 5 more than –2 times the input. Find the input when the output is 11. ANSWER –3

  20. for Examples 2 And 3 GUIDED PRACTICE 8. The output of a function is 4 less than 4 times the input. Find the input when the output is 3 3 ANSWER 1 4

  21. EXAMPLE 4 Solve a multi-step problem SCUBA DIVING As a scuba diver descends into deeper water, the pressure of the water on the diver’s body steadily increases. The pressure at the surface of the water is 2117 pounds per square foot (lb/ft2). The pressure increases at a rate of 64 pounds per square foot for each foot the diver descends. Find the depth at which a diver experiences a pressure of 8517 pounds per square foot.

  22. EXAMPLE 4 Solve a multi-step problem EXAMPLE 1 SOLUTION STEP 1 Write a verbal model. Then write an equation. STEP2 Find the depth at which the pressure is 8517 pounds per square foot. P = 2117 + 64d Write equation.

  23. EXAMPLE 4 Solve a multi-step problem GUIDED PRACTICE 8517 = 2117 + 64d Substitute 8517 for P. 8517 – 2117= 2117 – 2117 + 64d Subtract 2117 from each side. 6400 = 64d Simplify. 6400 64d Divide each side by 64. = 64 64 100 = d Simplify. ANSWER A diver experiences a pressure of 8517 pounds per square foot at a depth of 100 feet.

  24. EXAMPLE 4 Solve a multi-step problem GUIDED PRACTICE CHECK P= 2117 + 64d Write original equation. ? 85172117 + 64(100) = Substitute 8517 for P and 100 for d. ? 8517 2117 + 6400 Multiply 64 and 100. = 8517 = 8517 Simplify. Solution checks.

  25. for Example 4 GUIDED PRACTICE 9. WHAT IF?In Example 4, suppose the diver experiences a pressure of 5317 pounds per square foot. Find the diver’s depth. ANSWER 50 ft

  26. for Example 4 GUIDED PRACTICE Jobs 10. Kim has a job where she makes $8 per hour plus tips. Yesterday, Kim made $53 dollars, $13 of which was from tips. How many hours did she work? ANSWER 5 h

  27. Another Video

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