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Homework Answers: Workbook page 2

Homework Answers: Workbook page 2. N, W, Z, Q, R 13) Assoc. (X) 25) 8x – y – 3 I,R 14) Comm. (X) 26) -4c I, R 15) Add. Inverse 27) -5r – 58s W, Z, Q, R 16) Mult. Inverse 28) 4a + 1 Q, R 17) Distributive 29) -12 – 8x + 6y Z, Q, R 18) Add. Identity 30) 13y

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Homework Answers: Workbook page 2

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  1. Homework Answers: Workbook page 2 • N, W, Z, Q, R 13) Assoc. (X) 25) 8x – y – 3 • I,R 14) Comm. (X) 26) -4c • I, R 15) Add. Inverse 27) -5r – 58s • W, Z, Q, R 16) Mult. Inverse 28) 4a + 1 • Q, R 17) Distributive 29) -12 – 8x + 6y • Z, Q, R 18) Add. Identity 30) 13y • Z, Q, R 19) -0.4, 2.5 or 5/2 31) (110t + 100) mi • Q, R 20) 1.6, -0.625 or -5/8 32) false; counter- • Comm. (+) 21) 11/16, -16/11 example: • Assoc. (+) 22) -5 5/6, 6/35 5(1/5) is not > • Mult. Identity 23) 3x 4(1/4) • Distributive 24) -4a-16b

  2. Solving Equations Worksheet • K = -2 7) x = 19 • H = -4 8) x = 7 • D = -16/13 or -1.231 9) x = -1/15 or .0667 • J = -63/2 or -31.5 10) k = 18/23 or.7826 • X = 27 11) r = -5 • X = 36 12) g = -16

  3. Solving Equations with the Variable on Both Sides Objectives: • to solve equations with the variable on both sides. • to solve equations containing grouping symbols. • A.1 Solve linear equations in one variable. • A.1 Apply these skills to solve practical problems. • A.3 Justify steps used in solving equations.

  4. To solve equations with variables on both sides: 1. Use the addition property to move all variables to one side of the equal sign. 2. Solve the equation by working the problem backwards.

  5. 1) 6x - 3 = 2x + 13 -2x -2x 4x - 3 = 13 +3 +3 4x = 16 4 4 x = 4 Be sure to check your answer! 6(4) - 3 =? 2(4) + 13 24 - 3 =? 8 + 13 21 = 21 Let’s see a few examples:

  6. 2) 3n + 1 = 7n - 5 -3n -3n 1 = 4n - 5 +5 +5 6 = 4n 4 4 Reduce! 3 = n 2 Check: 3(1.5) + 1 =? 7(1.5) - 5 4.5 + 1 =? 10.5 - 5 5.5 = 5.5 Let’s try another!

  7. 3) 5 + 2(y + 4) = 5(y - 3) + 10 Distribute first. 5 + 2y + 8 = 5y - 15 + 10 Next, combine like terms. 2y + 13 = 5y - 5 Now solve. (Subtract 2y.) 13 = 3y - 5 (Add 5.) 18 = 3y (Divide by 3.) 6 = y Check: 5 + 2(6 + 4) =? 5(6 - 3) + 10 5 + 2(10) =? 5(3) + 10 5 + 20 =? 15 + 10 25 = 25 Here’s a tricky one!

  8. Let’s try one with fractions! • Steps: • Multiply each term • by the least common • denominator (8) to • eliminate fractions. • Solve for x. • Add 2x. • Add 6. • Divide by 6. 3 - 2x = 4x - 6 3 = 6x - 6 9 = 6x so x = 3/2

  9. 6(4 + y) - 3 = 4(y - 3) + 2y 24 + 6y - 3 = 4y - 12 + 2y 21 + 6y = 6y - 12 - 6y - 6y 21 = -12 Never true! 21 ≠ -12 NO SOLUTION! 3(a + 1) - 5 = 3a - 2 3a + 3 - 5 = 3a - 2 3a - 2 = 3a - 2 -3a -3a -2 = -2 Always true! We write ALL REAL NUMBERS. Two special cases:

  10. Try a few on your own: • 9x + 7 = 3x - 5 • 8 - 2(y + 1) = -3y + 1 • 8 - 1 z = 1 z - 7 2 4

  11. x = -2 y = -5 z = 20 The answers:

  12. Solving Formulas:What it means to solve • To solve for x would mean to get x by itself on one side of the equation, with no x’s on the other side. (x = __ ) • Similarly, to solve for y would mean to get y by itself on one side of the equation, with no y’s on the other side. (y = __ )

  13. 1) Solve the equation -5x + y = -56 for x. Ask yourself: What is the first thing being done to x, the variable being solved for? x is being multiplied by -5. DO UNDO ·-5 - y What is being done next? + y ÷(-5) y is being added to -5x. The DO-UNDO chart

  14. First, subtract y from both sides of the equation. Next, divide by -5. This process actually requires LESS WORK than solving equations in one variable  Ex: -5x + y = -56 - y -y -5x = -56 - y -5 -5 x = -56 - y = 56 + y -5 5 Show all of your work!

  15. Complete the do-undo chart. DO UNDO · 2 + 4y - 4y ÷ 2 To solve for x: First add 4y Then divide by 2 Ex: Solve 2x - 4y = 7 for x. 2x - 4y = 7 +4y + 4y 2x = 7 + 4y 2 2 x = 7 + 4y 2 This fraction cannot be simplified unless both terms in the numerator are divisible by 2. Let’s try another:

  16. Solve a(y + 1) = b for y. DO UNDO + 1 ÷ a · a - 1 To solve for y: First divide by a Then subtract 1 a(y + 1) = b a a y + 1 = b a - 1 -1 y = b - 1 a Another example:

  17. Solve 3ax - b = d - 4cx for x. First, we must get all terms with x together on one side. Add 4cx to both sides Add b to both sides Next, use the distributive property to factor x out of the two terms on the left. Now, x is being multiplied by (3a + 4c). To undo this, divide both sides by (3a + 4c). 3ax - b = d - 4cx +4cx +4cx 3ax - b + 4cx = d +b +b 3ax + 4cx = d + b x(3a + 4c) = d + b (3a + 4c) (3a + 4c) x = d + b (3a + 4c) Here’s a tricky one!

  18. Try a few on your own. • Solve P = 1.2W for W. H2 • Solve P = 2l + 2w for l. • Solve 4x - 3m = 2mx - 5 for x.

  19. DO UNDO · 1.2 · H2 ÷ H2 ÷ 1.2 W = PH2 1.2 DO UNDO · 2 -2w +2w ÷ 2 l = P - 2w 2 The answers: • Subtract 2mx, then • Add 3m to get • 4x - 2mx = 3m - 5 • x(4 - 2m) = 3m - 5 • Divide by (4 - 2m) • x = 3m - 5 4 - 2m

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