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Linear Equations in One Variable

Short Answer Type

121.

Solve for x:

$straight x minus fraction numerator 3 straight x over denominator 2 end fraction equals 35$

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122.

Solve for x:

$fraction numerator 3 straight x plus 10 over denominator 5 straight x plus 10 end fraction equals 5 over 7$

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123.

Solve for x:

$straight x squared plus 10 straight x plus 21 equals straight x squared plus 4 straight x plus 81$

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124.

A number is such that it is as much greater than 45 as it is less than 75. Find the number.

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125.

A number is 20 greater than the sum of its one-third and one-ninth. Find the number.

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126.
Divide 40 into two parts such that of one part is equal to of the other.

Let, the first part be x and the second part be y
Then,
1/4 x = 3/8 y
x = 3/2 y - (1)

Now,
x + y = 40
3/2 y + y = 40 - Putting the value of x from equation 1
(3y + 2y )/2 = 40
5y = 40 × 2
y = 80/5
y = 16

Now from equation 1,
x = 3/2 y
x = 3/2 × 16
x = 3 × 8
x = 24

Therefore, two parts are x = 24 and y = 16

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127.

The numerator of a fraction is 2 less than its denominator. If 2 is subtracted from the numerator and 1 is the added to the denominator then the fraction becomes 2/7. Find the fraction.

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