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Review Homework Page 163-165

Review Homework Page 163-165. 1. Write an equation for “ 3 more than twice a is 24. ”. 2 a + 3 = 24. ANSWER. 2 . A square has a side length of 8 feet. Find the area of the square using the formula A = s 2. 64 ft 2. ANSWER. Literal Equations page 166.

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Review Homework Page 163-165

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  1. Review HomeworkPage 163-165

  2. 1. Write an equation for “3 more than twice a is 24.” 2a + 3 = 24 ANSWER 2. A square has a side length of 8 feet. Find the area of the square using the formula A=s2. 64 ft2 ANSWER

  3. Literal Equations page 166

  4. 1) Solve 2x - 4y = 7 for xTo get x by itself, what is the first step? • Add 2x • Subtract 2x • Add 4y • Subtract 4y

  5. Ask yourself, What is the first thing we are doing to x? What is the second thing? 1) Solve 2x - 4y = 7 for xUse a DO-UNDO chart to help determine the steps DO UNDO · 2 -4y Follow the steps in the ‘undo’ column to isolate the variable. +4y ÷ 2 Complete the undo column by writing the opposite (inverse) operations in opposite order.

  6. D U 1) Solve 2x - 4y = 7 for x · 2 -4y +4y ÷ 2 + 4y = + 4y 2x = 7 + 4y 2 2 • Draw the center line (whatever we do on one side, we must do on the other) • Add 4y to both sides • Simplify • Divide both sides by 2 • Does it simplify? This fraction cannot be simplified because both terms in the numerator are not divisible by 2.

  7. 2) Solve 2x - 4y = 7 for yTo get y by itself, what is the first step? • Add 2x • Subtract 2x • Add 4y • Subtract 4y

  8. D U 2) Solve 2x - 4y = 7 for y · -4 +2x -2x ÷ -4 - 2x = - 2x -4y = 7 - 2x -4 -4 • Draw the center line • Subtract 2x from both sides • Simplify • Divide both sides by -4 • Does it simplify? Nope!

  9. 3) Solve for y: 4x – 2y = 12 • y = -4x + 12 • y = 4x - 12 • y = -2x + 6 • y = 2x - 6

  10. D U 3) Solve for y: 4x – 2y = 12 · -2 + 4x - 4x ÷ -2 - 4x - 4x -2y = 12 – 4x -2 -2 y = -6 + 2x or y = 2x - 6 • Draw the center line • Subtract 4x from both sides • Simplify • Divide both sides by -2 • Does it simplify? Yes!

  11. 4) The formula for the volume of a rectangular prism is V = LWH. Which equation solves the formula for L? • L = V - WH

  12. 5) The formula for the volume of a pyramid is V = . Which equation solves the formula for h? • h = 3Vb

  13. c ax + b = c – b ax = c – b x = a EXAMPLE Solve a literal equation Solve ax + b =cforx. Then use the solution to solve 2x + 5 = 11. a = 2, b = 5, c = 11 SOLUTION Solve ax + b = cfor x. STEP 1 Write original equation. Subtract bfrom each side. Assume a 0. Divide each side by a.

  14. x = = c – b 11– 5 = 3 a 2 The solution of 2x + 5 = 11 is 3. ANSWER EXAMPLE Solve a literal equation Usethe solution to solve 2x + 5 = 11. STEP 2 Solution of literal equation. Substitute 2 for a, 5 for b, and 11 for c. Simplify.

  15. ; 3 ANSWER c x= ; 4 ANSWER a–b x = a – c b PRACTICE Solve the literal equation for x. Then use the solution to solve the specific equation 1.a – bx =c; 12 – 5x = –3 2.ax =bx+ c; 11x = 6x + 20

  16. 3 2 3x + 2y 8 = 2y 8 – 3x = y = 4 – x EXAMPLE Rewrite an equation Write 3x + 2y = 8 so that yis a function of x. Solve for y. Write original equation. Subtract 3xfrom each side. Divide each side by 2.

  17. The area Aof a triangle is given by the formula A = bhwhere bis the base and his the height. 1 1 2 2 a. Solve the formula for the height h. b. Use the rewritten formula to find the height of the triangle shown, which has an area of 64.4 square meters. a. A bh = bh 2A = EXAMPLE 3 Solve and use a geometric formula SOLUTION Write original formula. Multiply each side by 2.

  18. 2A 2A = h b b b. Substitute 64.4 for Aand 14 for bin the rewritten formula. h = 2(64.4) = 14 ANSWER The height of the triangle is 9.2 meters. EXAMPLE 3 Solve and use a geometric formula Divide each side by b. Write rewritten formula. Substitute 64.4 for Aand 14 for b. =9.2 Simplify.

  19. 5 4 ANSWER y = 5 – x PRACTICE 3. Write 5x + 4y = 20 so that yis a function of x.

  20. The perimeter P ofa rectangle is given by the formula P =2l +2w where l is the length and w is the width. a. Solve the formula for the width w. 4 . P – 2l P ANSWER w = orw = – l 2 2 PRACTICE

  21. ANSWER 2.4 PRACTICE b . Use the rewritten formula to find the width of the rectangle shown.

  22. How to

  23. Practice • page 167

  24. Homework • Pages 168-170

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