Algebra 1 09/19-20/16 EQ: How do I solve Multi-Step Equations? HW: pg 89 # 1-35 odd, 81-89 all (all due on Wednesday) Bring textbooks tomorrow!!! HW sheet due this Friday Warm up: See board

Additional Example 1A: Solving Two-Step Equations Solve the equation. Check your answer. Since 2x + 1 is divided by 3, multiply both sides by 3 to undo the division. 2x + 1 = 21 Since 1 is added to 2x, subtract 1 from both sides to undo the addition. –1 –1 2x = 20 Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. x = 10 The solution set is {10}.

Additional Example 1B: Solving Two-Step Equations Solve the equation. Check your answer. Since 3x – 4 is divided by 2, multiply both sides by 2 to undo the division. Since 4 is subtracted from 3x, add 4 to both sides to undo the subtraction. +4 +4 18 = 3x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. 6 = x The solution set is {6}.

Check It Out! Example 1a Solve the equation. Check your answer. Since 5m + 13 is divided by 2, multiply both sides by 2 to undo the division. Since 13 is added to 5m, subtract 13 from both sides to undo the addition. 5m + 13 = 2 –13 –13 5m = –11 Since m is multiplied by 5, divide both sides by 5 to undo the multiplication. The solution set is .

You may have to combine like terms or use the Distributive Property before you begin solving.

Additional Example 2A: Simplifying Before Solving Equations Solve 8x – 21 – 5x = –15 8x – 21 – 5x = –15 Use the Commutative Property of Addition. Combine like terms. 8x – 5x – 21 = –15 3x – 21 = –15 Since 21 is subtracted from 3x, add 21 to both sides to undo the subtraction. +21 = +21 3x = 6 Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. x = 2 The solution set is {2}.

Additional Example 2B: Simplifying Before Solving Equations Solve 4 = 2x + 5 – 6x 4 = 2x + 5 – 6x Use the Commutative Property of Addition. Combine like terms. 4 = 2x – 6x + 5 4 = –4x + 5 –5 –5 –1 = –4x Since 5 is added to –4x, subtract 5 from both sides to undo the addition. Since x is multiplied by –4, divide both sides by –4 to undo the multiplication. The solution set is .

Check It Out! Example 2a Solve the equation. Check your answer. 2a + 3 – 8a = 8 Use the Commutative Property of Addition. Combine like terms. 2a – 8a +3 = 8 –6a + 3 = 8 Since 3 is added to –6a, subtract 3 from both sides to undo the addition. –3 –3 –6a = 5 Since a is multiplied by –6, divide both sides by –6 to undo the multiplication. The solution set is .

Check It Out! Example 2c Solve the equation. Check your answer. 4x – 8 + 2x = 40 4x – 8 + 2x = 40 Use the Commutative Property of Addition. Combine like terms. 4x + 2x – 8 = 40 6x – 8 = 40 Since 8 is subtracted from 6x, add 8 to both sides to undo the subtraction. +8 +8 6x = 48 Since x is multiplied by 6, divide both sides by 6 to undo the multiplication. x = 8 The solution set is {8}.

You can think of a negative sign as a coefficient of –1. –(x + 2) = –1(x + 2) and –x = –1x. Helpful Hint

Additional Example 3B: Simplify Using the Distributive Property Solve the equation. 10y – (4y + 8) = –20 Write subtraction as the addition of the opposite. 10y +(–1)(4y + 8) = –20 10y + (–1)(4y) + (–1)(8) = –20 Distribute –1. 10y – 4y – 8 = –20 Simplify. 6y – 8 = –20 Combine like terms. Since 8 is subtracted from 6y, add 8 to both sides to undo the subtraction. +8 +8 6y = –12

Additional Example 3B Continued Solve the equation. 10y – (4y +8) = –20 6y = –12 Since y is multiplied by 6, divide both sides by 6 to undo the multiplication. y = –2

Check It Out! Example 3a Solve the equation. Check your answer. 3(a + 1) – 4 = 5 3(a + 1) – 4 = 5 Distribute 3. (3)(a) + (3)(1) – 4 = 5 3a + 3 – 4 = 5 Simplify. Combine like terms. 3a – 1 = 5 Since 1 is subtracted from 3a, add 1 to both sides to undo the subtraction. + 1 +1 3a = 6 Since a is multiplied by 3, divide both sides by 3 to undo the multiplication. a = 2

Check It Out! Example 3b Solve the equation. Check your answer. –4(2 – y) = 8 –4(2 – y) = 8 Distribute –4 . (–4)(2) + (–4)(–y) = 8 Simplify. –8 + 4y = 8 Since –8 is added to 4y, add 8 to both sides. +8 +8 4y = 16 Since y is multiplied by 4, divide both sides by 4 to undo the multiplication. y = 4

Check It Out! Example 3c Solve the equation. Check your answer. d + 3(d – 4) = 20 d + 3(d – 4) = 20 d + 3(d) + 3(–4) = 20 Distribute 3. d + 3d – 12 = 20 Simplify. 4d – 12 = 20 Combine like terms. +12 +12 Since 12 is subtracted from 4d, add 12 to both sides to undo the subtraction. 4d = 32 Since d is multiplied by 4, divide both sides by 4 to undo the multiplication. d = 8