Find the value of A if (27\8)A+7=(4\9)-3A
(27\8)A+7=(4\9)-3A
=> (27/8)A + 3A = (4/9) - 7
=> A((27+24)/8) = (4-63)/7
=> (51/8)A = -59/7
=> A = -(59/7)*(8/51)
If (27\8)A+7=(4\9)-3A mean:
( 27 / 8 ) A + 7 = 4 / 9 - 3 A
then:
Add 3 A to both sides
27 A / 8 + 7 + 3 A = 4 / 9 - 3 A + 3 A
27 A / 8 + 7 + 24 A / 8 = 4 / 9
51 A / 8 + 7 = 4 / 9
Subtract 7 to both sides
51 A / 8 + 7 - 7 = 4 / 9 - 7
51 A / 8 = 4 / 9 - 63 / 9
51 A / 8 = - 59 / 9
Multiply both sides by 8
51 A = - 59 ∙ 8 / 9
51 A = - 472 / 9
Multiply both sides by 9
51 ∙ 9 A = - 472
459 A = - 472
Divide both sides by 459
A = - 472 / 459
But if 27 \ 8 mean the integer part of such a ratio ( integer division ) then:
( 27 \ 8 ) A + 7 = ( 4 \ 9 ) - 3 A
3 A + 7 = 0 - 3 A
3 A + 7 = - 3 A
Add 3 A to both sides
3 A + 7 + 3 A = - 3 A + 3 A
6 A + 7 = 0
Subtract 7 to both sides
6 A + 7 - 7 = 0 - 7
6 A = - 7
Divide both sides by 6
A = - 7 / 6
If possible, I prefer to work without fractions
(27\8)A+7=(4\9)-3A
times 72
243A + 504 = 32 - 216A
459A = -472
A = -472/459
I verified this answer in the left and right sides.
To find the value of A in the equation, we can follow these steps:
Step 1: Simplify the expression on the right side of the equation:
(4/9) - 3A
Step 2: Combining like terms, we get:
(4/9) - (27/9)A
Step 3: Convert the fraction (27/8) to the same denominator as (9/9):
(27/8) = (27/8) * (9/9) = (243/72)
Step 4: Substitute the simplified expression into the equation:
(243/72)A + 7 = (4/9) - (27/9)A
Step 5: Multiply both sides of the equation by the common denominator, which is 72:
243A + 504 = 32 - 27A
Step 6: Move the variable terms to one side of the equation and the constant terms to the other side:
243A + 27A = 32 - 504
Step 7: Combine the like terms on both sides of the equation:
270A = -472
Step 8: Divide both sides of the equation by 270 to isolate the variable A:
A = -472/270
Step 9: Simplify the fraction if possible:
A = -236/135
Hence, the value of A is -236/135.