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Linear Equations in One Variable

Short Answer Type

91.

Solve the following linear equation:

$x over 2 minus 1 fifth equals x over 3 plus 1 fourth$

106 Views

92.

Solve the following linear equation:

$straight n over 2 minus fraction numerator 3 straight n over denominator 4 end fraction plus fraction numerator 5 straight n over denominator 6 end fraction equals 21$

108 Views

93.

Solve the following linear equation:

$straight x plus 7 minus fraction numerator 8 straight x over denominator 3 end fraction equals 17 over 6 minus fraction numerator 5 straight x over denominator 2 end fraction$

120 Views

94.
Solve the following linear equation:

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∵ LCM of 3 and 5 is 15.

∴   Multiplying both sides by 15, we have

                    $15 cross times fraction numerator x minus 5 over denominator 3 end fraction equals 15 cross times fraction numerator x minus 3 over denominator 5 end fraction$

or                     5(x-5) = 3(x-3)

or                      5x - 25 = 3x - 9

Transposing (-25) to RHS and 3x to LHS, we have

                       5x -3x = -9 + 25

or                            2x = 16

or                              $x equals 16 over 2$          (Dividing both sides by 2)

∴ x = 8

 Check: LHS = $fraction numerator x minus 5 over denominator 3 end fraction$

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 = $3 over 3 equals 1$

 RHS = $space fraction numerator space straight x minus 3 over denominator 5 end fraction$

 = $fraction numerator 8 minus 3 over denominator 5 end fraction equals 5 over 5 equals 1$

∴ LHS = RHS

252 Views

95.

Solve the following linear equation:

$fraction numerator 3 t minus 2 over denominator 4 end fraction minus fraction numerator 2 t plus 3 over denominator 3 end fraction equals 2 over 3 minus t$

140 Views

96.

Solve the following linear equation:

$m minus fraction numerator m minus 1 over denominator 2 end fraction equals 1 minus fraction numerator m minus 2 over denominator 3 end fraction$