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Warm Up

Rewrite Equations and Formulas. Warm Up. Lesson Presentation. Lesson Quiz. 1. Evaluate . . 45 – 3(9). 4. or 4.5. ANSWER. y ( x – 5). x + y. 2. Evaluate when x = 3 and y = 5. x – 2 y. 8. 9. –. ANSWER. 7. 2. Warm-Up. ANSWER.

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Warm Up

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  1. Rewrite Equations and Formulas Warm Up Lesson Presentation Lesson Quiz

  2. 1.Evaluate . 45– 3(9) 4 or 4.5 ANSWER y(x – 5) x + y 2.Evaluate when x = 3 and y = 5. x – 2y 8 9 – ANSWER 7 2 Warm-Up ANSWER 3.Use the distributive property to rewrite xy – 5yas a product.

  3. Solve the formula for w. STEP 1 STEP 2 Substitute the given value into the rewritten formula. ANSWER The width of the rectangle is 8.5 meters. Example 1 Solve the formula P =2l+ 2w forw. Then find the widthw of the rectangle shown. SOLUTION P =2l+ 2w Write perimeter formula. P – 2l =2w Subtract 2lfrom each side. P – 2l = w Divide each side by 2. 2 41 –2(12) Substitute 41 for Pand 12 for l and simplify. = 8.5 w = 2

  4. A w = l Guided Practice 1. Solve the formula P =2l+ 2w forw. Then find the length of a rectangle with a width of 7 inches and a perimeter of 30 inches. ANSWER P – 2l = w The length of the rectangle is 8 inches. 2 2. Solve the formula A =lw forw. Then find the width of a rectangle with a length of 16 meters and an area of 40 square meters. ANSWER The width of the rectangle is 2.5 meters.

  5. Solve the formula for the variable in red. Then use the given information to find the value of the variable. 3. Find hif b = 12 m bh A = h = 2A b 1 2 Guided Practice and A = 84 m2. ANSWER

  6. h = 2A b Guided Practice Find the value of h if b = 12 m and A = 84 m2. Find hif b = 12 m and A = 84 m2. ANSWER h = 14 m

  7. Solve the formula for the variable in red. Then use the given information to find the value of the variable. 4. bh A = and A = 9 cm2. b = 2A h 1 2 Guided Practice Find bif h = 3 cm ANSWER

  8. b = 2A h Guided Practice Find the value ofbif h = 3 cmandA = 9 cm2. Find bif h = 3 cm and A = 9 cm2. ANSWER b = 6 cm

  9. Solve the formula for the variable in red. Then use the given information to find the value of the variable. (b1 + b2)h 5. Find hif b1 = 6in., A = b2 = 8in., and A = 70in.2 2A h= (b1 + b2) 1 2 Guided Practice ANSWER

  10. 2A h= (b1 + b2) Guided Practice Solve the formula for the variable in red. Then use the given information to find the value of the variable. Find hif b1 = 6in., b2 = 8in., and A = 70in.2 ANSWER h = 10 in.

  11. Solve ax + b = c for x . STEP 1 c – b a Example 2 Solve the literal equation ax + b = c for x.Then use your general solution to solve the equation –5 x – 9 = 12. SOLUTION ax + b = c Write original equation. ax = c – b Subtract bfrom each side. Divide each side bya (a 0). x =

  12. Example 2 Use the solution to solve –5 x – 9 = 12 by substituting –5for a, – 9for b,and 12 for cin the general solution. STEP 2 SOLUTION 12– (–9) c – b 21 –4.2 x = = = = – 5 a – 5

  13. d – b c – ab a – c a Guided Practice Solve the literal equation for x. Then use your general solution to solve the specific equation. 6. ax + b = cx + d; 5x + 2 = 3x + 10 ANSWER x= ; 4 7. a(x + b) = c; 4(x + 3) = 2 ANSWER x= ; –2.5

  14. Solve the equation for y. STEP 1 x y = + – 9 7 4 4 Example 3 Solve 9x – 4y = 7 for y. Then find the value ofywhen x= –5. SOLUTION 9x – 4y = 7 Write original equation. –4y = 7 – 9x Subtract 9xfrom each side. Divide each side by–4.

  15. (–5) 9(–5) – 4(–13) 7 45 – y = – 4 y = + – 7 9 7 4 4 4 ? = Example 3 Substitute the given value into the rewritten equation. STEP 2 Substitute–5 forx. Multiply. y = –13 Simplify. CHECK 9x– 4y= 7 Write original equation. Substitute–5 for xand–13 for y. 7 = 7 Solution checks.

  16. Solve the equation for y. STEP 1 6 y = 2 + x Example 4 Solve 2y + xy = 6 for y. Then find the value of ywhen x= –3. SOLUTION 2y + x y = 6 Write original equation. (2+ x) y = 6 Distributive property Divide each side by (2 + x).

  17. Substitute the given value into the rewritten equation. STEP 2 6 y = 2 + (–3) Example 4 Substitute –3 for x. y = –6 Simplify.

  18. ANSWER ANSWER ANSWER y = 7 + 6x + 6 y = 19 y = 5 y = 3 3x + y = 2 y = – x 13 5 5 Guided Practice Solve the equation for y. Then find the value of ywhen x = 2. 8. y – 6x = 7 9. 5y – x = 13 10. 3x + 2y = 12

  19. 1 4 ANSWER ANSWER ANSWER y = y = y = – 2x 28 3 +x 5 4 – x 2x y = –1 1 y = y = 14 –1 5 Guided Practice Solve the equation for y. Then find the value of ywhen x = 2. 12. 3 = 2xy – x 11. 2x + 5y = –1 13. 4y – xy = 28

  20. Example 5 Movie Rental A video store rents new movies for $5 and older movies for $3. • Write an equation that represents the store’s monthly revenue. • Solve the revenue equation for the variable representing the number of new movies rented. • The owner wants $12,000 in revenue per month. How many new movies must be rented if the number of older movies rented is 500? 1000?

  21. STEP 1 Write a verbal model. Then write an equation. Example 5 SOLUTION An equation is R = 5n1 + 3n2.

  22. =n1 R – 3n2 Calculate n1 for the given values of Rand n2. STEP 3 5 12,000 – 3 500 2100. = = 5 12,000 – 3 1000 = 5 1800. = Example 5 STEP 2 Solve the equation for n1. R = 5n1 + 3n2 Write equation. R – 3n2 = 5n1 Subtract 3n2 from each side. Divide each side by 5. Ifn2 = 500, thenn1 Ifn2 = 1000, thenn1 ANSWER If 500 older movies are rented, then 2100 new movies must be rented. If 1000 older movies are rented, then 1800 new movies must be rented.

  23. Guided Practice 14. What If?In Example 5, how many new movies must be rented if the number of older movies rented is 1500? ANSWER If 1500 older movies are rented, then 1500 new movies must be rented 15. What If?In Example 5, how many new movies must be rented if customers rent no older movies at all? ANSWER If 0 older movies are rented, then 2400 new movies must be rented.

  24. R – 5n1 3 n2= Guided Practice 16. Solve the equation in Step 1 of Example 5 for n2. ANSWER

  25. 1. The formula V = r2hgives the volume of a cylinder with radius rand height h. Solve this formula for h and then find the height of a cylinder with radius 8 centimeters and volume 704 cubic centimeters. π 21 y = ANSWER π 3 – x ANSWER V 11 cm h = ; r2 π y = 4 – x or y = – x + 4; 24 ANSWER 5 5 2 2 Lesson Quiz 2. Solve 5x + 2y = 8 for y. Then find the value of y when x = –8. 3. Solve 3y – xy = 21 for y.

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