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Warm Up

Solve Two-Step Equations. Warm Up. Lesson Presentation. Lesson Quiz. 2. b + 21 = 11. Warm-Up. Solve the equation. 1. 3 x = –18. –6. ANSWER. ANSWER. –10. 3. Simplify the expression 3 ( x + 2 ) – 4 x + 1. ANSWER. – x + 7. Warm-Up.

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Warm Up

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  1. Solve Two-Step Equations Warm Up Lesson Presentation Lesson Quiz

  2. 2. b+21 = 11 Warm-Up Solve the equation. 1. 3x= –18 –6 ANSWER ANSWER –10 3. Simplify the expression 3(x+2) – 4x+1. ANSWER –x + 7

  3. Warm-Up 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. ANSWER 7sheep

  4. Solve + 5 = 11. 11 + 5 = + 5 – 5 = 11 – 5 x x x x x 6 = 2 2 2 2 2 x = 12 2 = 2 6 ANSWER The solution is 12. Check by substituting 12 for xin the original equation. Example 1 Write original equation. Subtract 5 from each side. Simplify. Multiply each side by 2. Simplify.

  5. 11 ? 12 + 5 = 11 + 5 = 2 11 11 = x 2 Example 1 CHECK Write original equation. Substitute 12 for x. Simplify. Solution checks.

  6. 3. –1 = – 7 ANSWER ANSWER ANSWER 3 18 5 z 3 Guided Practice Solve the equation. Check your solution. 1. 5x + 9 = 24 2. 4y – 4= 16

  7. = 3x 21 3 3 Example 2 Solve7x – 4x = 21 7x – 4x = 21 Write original equation. 3x = 21 Combine like terms. Divide each side by 3. x = 7 Simplify.

  8. ANSWER ANSWER ANSWER 4 7 4 Guided Practice Solve the equation. Check your solution. 4. 4w + 2w = 24 5. 8t – 3t = 35 6. –16= 5d – 9d

  9. SOLUTION STEP1 Write an equation for the function. Let xbe the input and ybe the output Example 3 The output of a function is 3 less than 5 times the input. Find the input when the output is 17. y = 5x – 3 yis 3 less than 5 times x.

  10. 20 5x = 5 5 ANSWER STEP 2 An input of4 produces an output of17. Solve the equation for xwhen y =17. Example 3 y = 5x – 3 Write original function. 17 = 5x – 3 Substitute17 fory. 17 + 3= 5x – 3 +3 Add 3 to each side. 20 = 5x Simplify. Divide each side by5. 4 = x Simplify.

  11. ? 17 = 5(4) – 3 ? 17 = 20– 3 17 = 17 Example 3 CHECK y = 5x– 3 Write original function. Substitute 17 for yand 4 for x. Multiply 5 and 4. Simplify. Solution checks.

  12. 7. The output of a function is 5 more than –2 times the input. Find the input when the output is 11. 8. The output of a function is 4 less than 4 times the input. Find the input when the output is 3 ANSWER –3 3 ANSWER 1 4 Guided Practice

  13. 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. Example 4

  14. Example 4 SOLUTION STEP 1 Write a verbal model. Then write an equation.

  15. 6400 64d = 64 64 ANSWER A diver experiences a pressure of 8517 pounds per square foot at a depth of 100 feet. Example 4 STEP2 Find the depth at which the pressure is 8517 pounds per square foot. P = 2117 + 64d Write equation. 8517 = 2117 + 64d Substitute 8517 for P. 8517 – 2117= 2117 – 2117 + 64d Subtract 2117 from each side. 6400 = 64d Simplify. Divide each side by 64. 100 = d Simplify.

  16. 85172117 + 64(100) ? ? = = 8517 2117 + 6400 8517 = 8517 Example 4 CHECK P= 2117 + 64d Write original equation. Substitute 8517 for Pand 100 for d. Multiply 64 and 100. Simplify. Solution checks.

  17. 9. WHAT IF?In Example 4, suppose the diver experiences a pressure of 5317 pounds per square foot. Find the diver’s depth. 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 50 ft ANSWER 5 h Guided Practice Jobs

  18. a 4 1.+ 6 = –14 ANSWER – 80 ANSWER 3 – 3. 36 = 7y 2y + – 4 ANSWER Lesson Quiz Solve the equation. 2. 6r – 12 = 6

  19. 4. The output of a function is 9 less than 3 times the input. Write an equation for the function and then find the input when the output is –6. ANSWER 5. A bank charges $5.00 per month plus $0.30 per check for a standard checking account. Find the number of checks Justine wrote if she paid $8.30 in fees last month. y = 3x 9; 1 – ANSWER 11 checks Lesson Quiz

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