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Linear equation

by Dein
(Malaysia)











































Question 1 x/3 + x/2 + x/6 = 5

Question 2 x/8 = 2+x/5

Question 3 2x-1/3 - 3x+1/4 = x-6

Question 4 7y-1/9 - 6x-11/5 = 6/35

Comments for Linear equation

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Apr 09, 2011
Linear Equation
by: Staff

--------------------------------------------
Part II

Question 3: 2x - 1/3 - 3x + 1/4 = x - 6

2x - 1/3 - 3x + 1/4 = x - 6

Combine like terms

2x - 3x -1/3 +1/4 = x - 6

(2x - 3x) + (-1/3 +1/4) = x - 6

-x + (-1/3 +1/4) = x - 6

-x + [(-1/3)*(4/4) + (1/4)*(3/3)] = x - 6

-x + [(-4/12) + (3/12)] = x - 6

-x + (-1/12) = x - 6

-x - 1/12 = x - 6

Add x to each side of the equation

-x + x - 1/12 = x + x - 6

0 - 1/12 = x + x - 6

-1/12 = x + x - 6

-1/12 = 2x - 6

Add 6 to each side of the equation

-1/12 + 6 = 2x - 6 + 6

-1/12 + 6 = 2x + 0

-1/12 + 6 = 2x

-1/12 + 6*(12/12) = 2x

-1/12 + 72/12 = 2x

-1/12 + 72/12 = 2x

71/12 = 2x

Divide each side of the equation by 2

(71/12) ÷ 2 = 2x ÷ 2

(71/12) ÷ 2 = 2x/2

(71/12) ÷ 2 = x * (2/2)

(71/12) ÷ 2 = x * (1)

(71/12) ÷ 2 = x * 1

(71/12) ÷ 2 = x

(71/12)/(2/1) = x

(71/12)*(1/2) = x

(71 * 1)/(12 * 2) = x

(71)/(24) = x

71/24 = x


Question 4: 7y - 1/9 - 6x - 11/5 = 6/35

7y - 1/9 - 6x - 11/5 = 6/35

Combine like terms

7y - 6x + (-1/9 - 11/5) = 6/35

7y - 6x + [(-1/9)*(5/5) + (-11/5)*(9/9)] = 6/35

7y - 6x + [(-5/45) + (-99/45)] = 6/35

7y - 6x + (-104/45) = 6/35

7y - 6x - 104/45 = 6/35

Add 104/45 to each side of the equation

7y - 6x - 104/45 + 104/45 = 6/35 + 104/45

7y - 6x + 0 = 6/35 + 104/45

7y - 6x = 6/35 + 104/45

7y - 6x = (6/35)*(45/45) + (104/45)*(35/35)

7y - 6x = (6*45)/(35*45) + (104*35)/(45*35)

7y - 6x = (270)/(1575) + (3640)/(1575)

7y - 6x = 270/1575 + 3640/1575

7y - 6x = (270 + 3640)/1575

7y - 6x = (3910)/1575

7y - 6x = 3910/1575

7y - 6x = (782*5)/(315*5)

7y - 6x = (782/315)*(5/5)

7y - 6x = (782/315)*(1)

7y - 6x = (782/315)*1

7y - 6x = (782/315)

7y - 6x = 782/315

Add 6x to each side of the equation

7y - 6x + 6x = 782/315 + 6x

7y + 0 = 782/315 + 6x

7y = 782/315 + 6x

7y = 6x + 782/315

Divide each side of the equation by 7

7y/7 = (6x + 782/315)/7

y*(7/7) = (6x + 782/315)/7

y*(1) = (6x + 782/315)/7

y*1 = (6x + 782/315)/7

y = (6x + 782/315)/7

use the distributive law to eliminate the parentheses on the right side of the equation.

y = 6x/7 + (782/315)*(1/7)

y = 6x/7 + 782/(315*7)

y = 6x/7 + 782/2205



The final answers are:


Question 1: x/3 + x/2 + x/6 = 5

x = 5



Question 2: x/8 = 2+x/5

x = -26⅔ = -26.6667



Question 3: 2x-1/3 - 3x+1/4 = x-6

x = 71/24 = 2.958333



Question 4: 7y-1/9 - 6x-11/5 = 6/35

y = 6x/7 + 782/2205

y = 0.857143x + 0.354649





Thanks for writing.


Staff
www.solving-math-problems.com


Apr 09, 2011
Linear Equation
by: Staff

Part I

The question:

by Dein
(Malaysia)

Question 1: x/3 + x/2 + x/6 = 5

Question 2: x/8 = 2 + x/5

Question 3: 2x - 1/3 - 3x + 1/4 = x - 6

Question 4: 7y - 1/9 - 6x - 11/5 = 6/35

The answer:

Question 1: x/3 + x/2 + x/6 = 5

Find a common denominator for the three fractions, then add the fractions:

x/3 + x/2 + x/6 = 5

(x/3)*(2/2) + (x/2)*(3/3) + x/6 = 5

(2x/6) + (3x/6) + x/6 = 5

2x/6 + 3x/6 + x/6 = 5

(2x + 3x + x)/6 = 5

(6x)/6 = 5

x*(6/6) = 5

x*(1) = 5

x*1 = 5

x = 5


Question 2: x/8 = 2+x/5

x/8 = 2+x/5

Multiply each side of the equation by 8*5. This will eliminate the fractions.

(x/8)*(8*5) = (2 + x/5)*(8*5)

5x*(8/8) = (2 + x/5)*(8*5)

5x*(1) = (2 + x/5)*(8*5)

5x*1 = (2+x/5)*(8*5)

5x = (2+x/5)*(8*5)

Using the distributive law

5x = (2*8*5) + (x/5)*(8*5)

5x = (2*8*5) + (8x)*(5/5)

5x = (2*8*5) + (8x)*(1)

5x = (2*8*5) + (8x)*1

5x = (2*8*5) + (8x)

5x = (2*8*5) + 8x

5x = (80) + 8x

5x = 80 + 8x


Subtract 5x from each side of the equation

5x - 5x = 80 + 8x - 5x

0 = 80 + 8x - 5x

0 = 80 + 3x

Subtract 80 from each side of the equation

0 - 80 = 80 - 80 + 3x

0 - 80 = 0 + 3x

0 - 80 = 3x

-80 = 3x

Divide each side of the equation by 3

-80/3 = 3x/3

-80/3 = x*(3/3)

-80/3 = x*(1)

-80/3 = x*1

-80/3 = x

-26⅔ = x


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