Download - Solving ax + b = cx+d
Practice ProblemFive more than three times a number is three more than 5 times the number. What is the number??
Objective- To solve equations in the form ax + b = cx + d and inequalities
in the form ax + b < cx + dSolve.
14k + 20 = 21k - 43-14k -14k
20 = 7k - 43+ 43 + 43
63 = 7k7 79 = k
Solve.
x + 1.05x = 2x - 1000
2.05x = 2x - 1000-2x -2x
0.05x = -10000.05 0.05
x = -20,000
Solve.
- 2y + 11 = - 6y+2y +2y
11 = - 4y- 4 - 4
-2.75 = y
ProblemIn 1990, the population of El Paso was515,000 and increasing at 9000 peopleper year. Milwaukee was 628,000 anddecreasing at 800 people per year. When will they be the same?
Let n = number of yearsLet P = population
El Paso Milwaukee
P = 515,000 + 9000n P = 628,000 - 800n
Let n = number of years Let P = populationEl 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 = 113,0009800 9800
n 11.53 years
Problems Involving InequalitiesSolve.
-3( x - 5 ) + 7 < 4( 3x + 2)-3x + 15 + 7 < 12x + 8
-3x + 22 < 12x + 8+3x +3x
22 < 15x + 8- 8 - 8
14 < 15x15 15
< x14
15
x >14
15
Tree ProblemA beech tree is 8 ft. tall and grows ft. per year. A maple tree is 3 ft. tall and grows 1 foot per year. Whenwill the maple be taller than the beech?
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2
Let x = number of years
Let h = height of tree
Beech tree Maple treeh = 8 + 0.5x h = 3 + x
Let x = number of yearsLet h = height of tree
Beech tree Maple treeh = 8 + 0.5x h = 3 + x
When is maple taller than beech?
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8 + 0.5x < 3 + x- 0.5x - 0.5x
8 < 3 + 0.5x5 < 0.5x
10 < x x > 10 years