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Linear Equations In One Variable

Question
CBSEENMA8002375
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Solve for straight x colon fraction numerator 7 straight x plus 14 over denominator 3 end fraction minus fraction numerator 17 minus 3 straight x over denominator 5 end fraction equals 6 straight x minus fraction numerator 4 straight x plus 2 over denominator 3 end fraction minus 5

Solution

We have fraction numerator 7 straight x plus 14 over denominator 3 end fraction minus fraction numerator 17 minus 3 straight x over denominator 5 end fraction equals 6 straight x minus fraction numerator 4 straight x plus 2 over denominator 3 end fraction minus 5
   Since, LCM of 3 and 5 is 15.

∴      The given equation is expressed as:
          space space fraction numerator 5 left square bracket 7 x plus 14 right square bracket over denominator 5 cross times 3 end fraction minus fraction numerator 3 left square bracket 17 minus 3 x right square bracket over denominator 3 cross times 5 end fraction equals open parentheses fraction numerator 15 cross times 6 x over denominator 15 end fraction close parentheses minus fraction numerator 5 left parenthesis 4 x plus 2 right parenthesis over denominator 5 cross times 3 end fraction minus open parentheses fraction numerator 15 cross times 5 over denominator 15 end fraction close parentheses
rightwards double arrow          fraction numerator 35 straight x plus 70 over denominator 15 end fraction minus fraction numerator left parenthesis 51 minus 9 straight x right parenthesis over denominator 15 end fraction equals fraction numerator 90 straight x over denominator 15 end fraction minus fraction numerator left parenthesis 20 straight x plus 10 right parenthesis over denominator 15 end fraction minus 75 over 15
rightwards double arrow           35x + 70 - (51-9x) = 90x - (20x + 10) - 75
rightwards double arrow              35x + 70 -51 + 9x = 90x - 20x - 10 - 75
rightwards double arrow            35x + 9x - 90x + 20x = -10 -75 + 51 - 70
rightwards double arrow                        64x - 90x = -155 + 51
rightwards double arrow                             -26x = -104
rightwards double arrow                               straight x equals fraction numerator negative 104 over denominator negative 26 end fraction equals 4
   Thus, x = 4 is the solution of the given equation.
  


Some More Questions From Linear Equations in One Variable Chapter

Solve the following equations:

x - 2 = 7

Solve the following equation:

6 = z + 2

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