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2.3 Solve two-step equations

2.3 Solve two-step equations. You will solve two-step equations. Essential question: How do you solve two-step equations?. 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.

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2.3 Solve two-step equations

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  1. 2.3 Solve two-step equations • You will solve two-step equations • Essential question: How do you solve two-step equations?

  2. 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 Solve a two-step equation Write original equation. Subtract 5 from each side. Simplify. Multiply each side by 2. Simplify.

  3. 11 ? 12 + 5 = 11 + 5 = 2 11 11 = x 2 EXAMPLE 1 Solve a two-step equation CHECK Write original equation. Substitute 12 for x. Simplify. Solution checks.

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

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

  6. 3. –1 = – 7 ANSWER 18 z 3 for Example 1 GUIDED PRACTICE Solve the equation. Check your solution.

  7. = 3x 21 3 3 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. Divide each side by 3. x = 7 Simplify.

  8. SOLUTION STEP1 Write an equation for the function. Let xbe the input and ybe the output STEP 2 Solve the equation for xwhen y =17. 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. y = 5x – 3 yis 3 less than 5 times x.

  9. 20 5x = 5 5 ANSWER An input of4 produces an output of17. EXAMPLE 3 Find an input of a function 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.

  10. ? 17 = 5(4) – 3 ? 17 = 20– 3 17 = 17 EXAMPLE 3 Find an input of a function CHECK y = 5x– 3 Write original function. Substitute 17 for yand 4 for x. Multiply 5 and 4. Simplify. Solution checks.

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

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

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

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

  15. 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 for Examples 2 And 3 GUIDED PRACTICE

  16. 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 Solve a multi-step problem

  17. 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.

  18. 6400 64d = 64 64 ANSWER A diver experiences a pressure of 8517 pounds per square foot at a depth of 100 feet. 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. Divide each side by 64. 100 = d Simplify.

  19. 85172117 + 64(100) ? ? = = 8517 2117 + 6400 8517 = 8517 EXAMPLE 4 Solve a multi-step problem GUIDED PRACTICE CHECK P= 2117 + 64d Write original equation. Substitute 8517 for Pand 100 for d. Multiply 64 and 100. Simplify. Solution checks.

  20. 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 for Example 4 GUIDED PRACTICE

  21. 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 for Example 4 GUIDED PRACTICE Jobs

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

  23. 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 $.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 Daily Homework Quiz

  24. You will solve two-step equations • Essential question: How do you solve two-step equations? • To solve equations efficiently, apply inverse operations in the reverse order of the operations performed on the variable. • Combine like terms before solving equations. First look for like terms and combine them when solving two-step equations. For equations with tow operations, look at the original equation and apply the inverse operations in the reverse order.

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