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Linear Equations in One Variable

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Class 10 Class 12

Find the solution of 3x-2=13.


3x-2=13

Transposing -2 to RHS, we have

Or                              3x=13+2

                                 3x=15

Or                               x=15 over 3               (Dividing both sides by 3)

Or                               x=5

1141 Views

If 1 is subtracted from both sides of x + 1 = 5, then we have:

  • x = 5 – 1

  • x + 2 4

  • x = 1 – 6


A.

x = 5 – 1

153 Views

If 1 is added to both sides of x – 1 = 18, then we have:

  • x – 1 + 1 = 18 – 1

  • x – 1 + 1 = 18 + 1

  • x – 1 + 1 = 18 – 2


B.

x – 1 + 1 = 18 + 1

125 Views

Solve:   fraction numerator x plus 3 over denominator 6 end fraction plus 1 space equals space fraction numerator 6 x minus 1 over denominator 3 end fraction


fraction numerator x plus 3 over denominator 6 end fraction plus 1 space equals space fraction numerator 6 x minus 1 over denominator 3 end fraction

Multiplying both sides by 6, we have             (∵   LCM of 3 and 6 is 6)

         6 cross times fraction numerator x plus 3 over denominator 6 end fraction plus 6 cross times 1 equals 6 cross times fraction numerator 6 x minus 1 over denominator 3 end fraction

or             x + 3 + 6 = 2(6x-1)

or                x + 9 = 12x - 2

    Transposing 9 to RHS and 12x to LHS, we have
                
                       x - 12x = -2 - 9
or                    -11x = -11

or                     x equals fraction numerator negative 11 over denominator negative 11 end fraction equals 1   (Dividing both sides by (-11))

∴                       x = 1

Check:         LHS = fraction numerator x plus 3 over denominator 6 end fraction plus 1 equals fraction numerator 1 plus 3 over denominator 6 end fraction plus 1

                               equals space 4 over 6 plus 1 equals space 2 over 3 plus 1
equals fraction numerator 2 plus 3 over denominator 3 end fraction equals 5 over 3

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                                          equals fraction numerator 6 minus 1 over denominator 3 end fraction equals 5 over 3

∴                          LHS = RHS






           


       

 

 




142 Views

The digits of a two digit number differ by 5. If the digits are interchanged and the resulting number is added to the original number, then we get 99. Find the original number.


Let the digit at unit place be 'x'.

∴                    The digit at the tens place = (x+5)

∴                                original number =10(x+5) + x
   
        With interchange of digits, the new number = 10x + (x + 5)
  
     Now, According to the condition, we have

             [original number] + [New number] = 99

or         [10(x + 5) + x] + [10x + (x + 5)] = 99

or         [10x + 50 +x] + [10x + x + 5] = 99

or                        11x + 50 + 11x + 5 = 99

or                                       22x + 55 = 99

    Transposing 55 to RHS, we have
                                                  22x = 99 - 55 = 44

    Dividing both sides by 22, we have
                                               x = 44 divided by22 = 2

∴                                              x = 2

i.e.                                Unit place digit = 2

∴                                 Tens place digit = 2 + 5 = 7

                            Thus the original number = 72.



                                               

278 Views

If x – 1 = 6, then x = ?

  • x = 6 + 1

  • x = 6 - 1

  • x = 1 – 6


A.

x = 6 + 1

125 Views