solve the equation:
1. 1/2a+2/3=(-1/3)a-3/4
To solve the equation (1/2a) + (2/3) = (-1/3)a - (3/4), we need to isolate the variable 'a' on one side of the equation.
Step 1: Remove the fractions by multiplying every term by the least common denominator (LCD) of all the fractions involved. In this case, the LCD is 12, as it is the least common multiple of 2, 3, and 4.
Multiplying each term by 12 to clear the fractions:
12 * (1/2a) + 12 * (2/3) = 12 * (-1/3)a - 12 * (3/4)
Simplifying the equation:
6a + 8 = -4a - 9
Step 2: Move all the 'a' terms to one side of the equation and the constant terms to the other side. We can do this by adding 4a to both sides and adding 9 to both sides.
6a + 4a + 8 = -4a + 4a - 9
Simplifying the equation:
10a + 8 = -9
Step 3: Move the constant term to the other side of the equation by subtracting 8 from both sides.
10a + 8 - 8 = -9 - 8
Simplifying the equation:
10a = -17
Step 4: Solve for 'a' by dividing both sides of the equation by 10.
(10a)/10 = (-17)/10
Simplifying the equation:
a = -17/10
Therefore, the solution to the equation (1/2a) + (2/3) = (-1/3)a - (3/4) is a = -17/10.