.. (18. Cor. 1.) 21x 39 = 10x + 5;

.. (17) by transposition, 21 x - 10x = 39 + 5,

24. Given 12 - x ::: 4 : 1, to find the value of x.

2

(21) Since the product of the extremes is equal to the product of the means,

.. (17) by transposition, 12 = 2x + x = 3x,

:: 7:4, to find the value of x.

.. (18. Cor. 2.) 40x + 32 = 126-7x; .. (17) by transposition, 40x + 7x = 126

32,

26. Given (4x + 16) = 12, to find the value of x.

(19) squaring both sides of the equation, 4x + 16 = 144;

.. (17) by transposition, 4x = 144 - 16 = 128;

.. (18. Cor. 2.) x = 32.

128

4

27. Given (2x + 3) + 4 = 7, to find the value of x.

(17) by transposition, ☑ (2x + 3) = 7 - 4 = 3;

... (19) cubing both sides of the equation, 2x + 3 = 27; .. (17) by transposition, 2x = 27 - 3 = 24,

28. Given

(12 + x) = 2 + ✓ x, to find the value of x.

(19) squaring both sides of the equation,

12 + x 4+4 x + x;

.. (17. Cor. 3.) 8 = 4√x;

and (18. Cor. 2.) 2 = √x;

x, to find the value

.. (18. Cor. 1.) 21x - 39 = 10x + 5;

.. (17) by transposition, 21 - 10x = 39 + 5,

50 12
126x 522
50 -12

13,

.. (17. Cor. 3.)
and (18. Cor. 1.) 126x - 522 = 65X - 156;
(17) by transposition, 61 x = 366;
.. (18. Cor. 2.) х

366
61

6.

:: 4 : 1, to find the value of x.

(21) Since the product of the extremes is equal to the product of the means,

.. (17) by transposition, 12 = 2x + x = 3x,

:: 7: 4, to find the value of x.

.. (18. Cor. 2.) 40x + 32 = 126 - 7x;

.. (17) by transposition, 40x + 7x = 126 - 32,

or 47 x = 94;

94

..x = = 2.

47

26. Given (4x + 16) = 12, to find the value of x.

(19) squaring both sides of the equation, 4x + 16 = 144 ;

.. (17) by transposition, 4x = 144 - 16 = 128;

27. Given

(2x + 3) + 4 = 7, to find the value of x.

(17) by transposition, ☑ (2x + 3) = 7 - 4 = 3; ... (19) cubing both sides of the equation, 2x + 3 = 27;

.. (17) by transposition, 2x = 27

3 = 24,

(x + 40) = 10 ✓ x, to find the value

29. Given

(19) squaring both sides of the equation,

x 16 = 64 16√x + x;

.. (17. Cor. 3.) 16 ✓ x = 64 + 16 = 80;

31. Given

.. (18. Cor. 2.) ✓ = 5,

and (19) x = 25.

(x-24) = √x - 2, to find the value of x.

(19) squaring both sides of the equation,

(19) squaring both sides of the equation,

33. Given x (x + 2) = (19) squaring both sides of the equation,

4