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?

1

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?

<

8 + 0.5x < 3 + x- 0.5x - 0.5x

8 < 3 + 0.5x5 < 0.5x

10 < x x > 10 years