Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Solve each equation. 1. 15x = 225 2. y + 2 = 10 Find the value of each expression. 3. 18 – 6 3  5 4. 7 + 3  (16  4) – 2 x = 15 y = 8 8 17

Problem of the Day Janet used a pedometer to count her steps. The first day and third day she took exactly the same number of steps. The second day she took 1,739 steps. If she took 6,125 steps in all those 3 days, how many steps did she take the first day? 2,193 steps

Sunshine State Standards MA.6.A.3.3 Works backward with two-step functions rules to undo expressions. Also MA.6.A.3.2

Additional Example 1A: Solving Two-Step Equations Solve each equation. 18 + 3x = 30 18 + 3x = 30 – 18 –18 Subtract 18 from both sides to undo the addition. 3x = 12 3x 3 = 12 Divide both sides by 3 to undo the multiplication. x = 4

Additional Example 1A Continued Check 18 + 3x = 30 Substitute 4 for x in the equation. 18 + 3(4) ? = 30 18 +12 30 ? = 30 30 ? = 4 is the solution.

Undo operations in the reverse of the Order of Operations Undo operations in the reverse of the Order of Operations. First undo addition or subtraction. Then undo multiplication or division. Helpful Hint

Additional Example 1B: Solving Two-Step Equations Solve. Check the answer. x 3 – 2 = 1 x 3 – 2 = 1 Add 2 to both sides to undo the subtraction. + 2 +2 x 3 = 3 3 · = 3 · 3 x 3 Multiply both sides by 3. x = 9

Additional Example 1B Continued Check x 3 – 2 = 1 9 3 Substitute 9 for x in the equation. ? = – 2 1 ? = 3 – 2 1 ? = 1 1 9 is the solution.

Additional Example 1C: Solving Two-Step Equations Solve. Check the answer. x + 19 4 = 6 x + 19 4 Multiply both sides by 4 to undo the division. 4 · = 4 · 6 x + 19 = 24 Subtract both sides by 19 to undo the addition. – 19 – 19 x = 5

Additional Example 1C Continued Check x + 19 4 = 6 Substitute 5 for x in the equation. 5 + 19 4 = 6 24 4 6 ? = 6 6 ? = 5 is the solution.

Check It Out: Example 1A Solve each equation . 7 x – 5 = 23 + 5 +5 x = 4 7x 7 7 x 28 =

Check It Out: Example 1B Solve each equation . x – 16 = 9 3 x – 16 = 9 + 16 +16 x = 75 x 3 25 = 3 · 3 · 25

Check It Out: Example 1C Solve. Check the answer. x - 9 10 = 49 10 · =10 · 49 +9 +9 =490 x - 9 10 x 499 =

Additional Example 2: Consumer Math Application Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy? Write a two-step equation to represent the situation. Let x represent the number of CDs Nancy can buy. cost of a CD times the number of CDs cost of headphones total cost + = 15x + 12 = 87 The equation 15x + 12 = 87 represents the situation.

Additional Example 2 Continued Nancy saved $87 of the money she made babysitting. She wants to buy CDs that cost $15 each, along with a set of headphones that costs $12. How many CDs can she buy? Solve the equation. 15x + 12 = 87 – 12 –12 Subtract 12 from both sides. 15x = 75 15x = 75 Divide both sides by 15. 15 15 x = 5 Nancy can buy 5 CDs.

Check It Out: Example 2 Kaia earned $425 last week. She wants to put $350 in the bank and buy some DVDs. Each DVD costs $25. Write a two-step equation to represent the situation. Then solve the equation. How many DVDs can she buy? Let x represent the number of DVDs purchased. 25x + 350 = 425 - 350 = - 350 25x 75

Check It Out: Example 2 Continued 75 = 25 25 x = 3 Kaia can buy 3 DVDs.

Additional Example 3: Working Backward with Function Rules The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11. The function rule is 5 times input minus 4 equals output 5 x x – 4 = y

Additional Example 3 Continued The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11. Use the function rule and the given output value to write an equation. 5x – 4 = 11 Add 4 to both sides to undo the subtraction. + 4 + 4 5x = 15 5x = 15 Divide both sides by 5. 5 5 x = 3 The input value is 3.

Additional Example 3 Continued The rule for a certain function is to multiply the input by 5 and subtract 4. Find the input value when the output is 11. Check Substitute the input value into the rule. 5(3) – 4 = 15 – 4 = 11 check

The function rule is x – 8 = y 2 – 8 = 3 Check It Out: Example 3 The rule for a certain function is to multiply the input by 2 and subtract 8. Find the input value when the output is 3. The function rule is x – 8 = y 2 x 2 – 8 = 3 + 8 + 8 x 2 = 11 x 2 2 = 2 11

Check It Out: 3 Continued x = 22 The input value is 22.