To solve this equation, we must first clear the parentheses and simplify both sides:
(5а - 0.5)/4 - (3 + 4а)/5 = (4 - 7а)/3 - (11а - 1.5)/6
First, simplify the left side of the equation:
(5а - 0.5)/4 - (3 + 4а)/5= (5а - 0.5)/4 - (3/5 + 4а/5)= (5а - 0.5)/4 - (3/5 + 4а/5)= (5а - 0.5)/4 - ((3 + 4а)/5)= (5а - 0.5)/4 - (3 + 4а)/5= (5a - 0.5)5 - (4(3 + 4a))/20= (5а - 0.5)5 - (3 + 4а)/5= 5а - 2.5 - 3 - 4а= а - 5.5
Next, simplify the right side of the equation:
(4 - 7а)/3 - (11а - 1.5)/6= (4/3 - 7а/3) - (11а/6 - 1.5/6)= (4/3 - 7а/3) - (11а/6 - 1.5/6)= (4/3 - 7а/3) - (11а/6 - 1.5/6)= (4 - 7а*2) - (11а - 1.5)/6= (4 - 14а) - (11а - 1.5)/6= 4 - 14а - 11а + 1.5= -25а + 5.5
So, the simplified equation is:а - 5.5 = -25а + 5.5
Next, let's solve for 'a'.
Adding 25a to both sides:
26a - 5.5 = 5.5
Adding 5.5 to both sides:
26a = 11
Dividing by 26:
a = 11 / 26
Therefore, the solution to the equation is a = 11/26.
To solve this equation, we must first clear the parentheses and simplify both sides:
(5а - 0.5)/4 - (3 + 4а)/5 = (4 - 7а)/3 - (11а - 1.5)/6
First, simplify the left side of the equation:
(5а - 0.5)/4 - (3 + 4а)/5
= (5а - 0.5)/4 - (3/5 + 4а/5)
= (5а - 0.5)/4 - (3/5 + 4а/5)
= (5а - 0.5)/4 - ((3 + 4а)/5)
= (5а - 0.5)/4 - (3 + 4а)/5
= (5a - 0.5)5 - (4(3 + 4a))/20
= (5а - 0.5)5 - (3 + 4а)/5
= 5а - 2.5 - 3 - 4а
= а - 5.5
Next, simplify the right side of the equation:
(4 - 7а)/3 - (11а - 1.5)/6
= (4/3 - 7а/3) - (11а/6 - 1.5/6)
= (4/3 - 7а/3) - (11а/6 - 1.5/6)
= (4/3 - 7а/3) - (11а/6 - 1.5/6)
= (4 - 7а*2) - (11а - 1.5)/6
= (4 - 14а) - (11а - 1.5)/6
= 4 - 14а - 11а + 1.5
= -25а + 5.5
So, the simplified equation is:
а - 5.5 = -25а + 5.5
Next, let's solve for 'a'.
Adding 25a to both sides:
26a - 5.5 = 5.5
Adding 5.5 to both sides:
26a = 11
Dividing by 26:
a = 11 / 26
Therefore, the solution to the equation is a = 11/26.