(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)
Find the value of A if (27\8)A+7=(4\9)-3A
3 answers
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
( 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.
(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.