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# Solving ax + b = cx+d

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Solving linear equations of the form ax + b = cx + d

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### Solving ax + b = cx+d

1. 1. Practice Problem Five more than three times a number is three more than 5 times the number. What is the number??
2. 2. Objective- To solve equations in the form ax + b = cx + d and inequalities in the form ax + b < cx + d Solve. 14k + 20 = 21k - 43 -14k -14k 20 = 7k - 43 + 43 + 43 63 = 7k 7 7 9 = k
3. 3. Solve. x + 1.05x = 2x - 1000 2.05x = 2x - 1000 -2x -2x 0.05x = -1000 0.05 0.05 x = -20,000
4. 4. Solve. - 2y + 11 = - 6y +2y +2y 11 = - 4y - 4 - 4 -2.75 = y
5. 5. Problem In 1990, the population of El Paso was 515,000 and increasing at 9000 people per year. Milwaukee was 628,000 and decreasing at 800 people per year. When will they be the same? Let n = number of years Let P = population El Paso Milwaukee P = 515,000 + 9000n P = 628,000 - 800n
6. 6. Let n = number of years Let P = population El Paso Milwaukee P = 515,000 + 9000n P = 628,000 - 800n 515,000 + 9000n = 628,000 - 800n + 800n +800n 515,000 + 9800n = 628,000 -515,000 -515,000 9800n = 113,000 9800 9800 n 11.53 years
7. 7. Problems Involving Inequalities Solve. -3( x - 5 ) + 7 < 4( 3x + 2) -3x + 15 + 7 < 12x + 8 -3x + 22 < 12x + 8 +3x +3x 22 < 15x + 8 - 8 - 8 14 < 15x 15 15 < x x >
8. 8. Tree Problem A beech tree is 8 ft. tall and grows ft. per year. A maple tree is 3 ft. tall and grows 1 foot per year. When will the maple be taller than the beech? Let x = number of years Let h = height of tree Beech tree Maple tree h = 8 + 0.5x h = 3 + x
9. 9. Let x = number of years Let h = height of tree Beech tree Maple tree h = 8 + 0.5x h = 3 + x When is maple taller than beech? < 8 + 0.5x < 3 + x - 0.5x - 0.5x 8 < 3 + 0.5x 5 < 0.5x 10 < x x > 10 years