3x-2 + 2-x = - 1
---- ---- --
8 4 2
correction
3x-2/8 + 2-x/ 4 = - 1/2
(3x-2)/8 + (2-x)/ 4 = - 1/2
easy way: clear fractions by multiplying by 8:
(3x-2) + 2(2-x) = (-1/2)(4)
3x-2+4-2x = -2
x+2 = -2
x = -6
check:
(3(-6)-2)/8 + (2-(-6))/4 = -20/8 + 8/4 = -5/2 + 2 = -1/2
To solve the equation (3x-2)/(8) + (2-x)/(4) - 1/(2) = 0, we can follow these steps:
1. Simplify each fraction individually:
(3x-2)/(8) can be left as it is.
(2-x)/(4) can be rewritten as -(x-2)/(4) because dividing numerator and denominator by -1 gives the same fraction.
-1/(2) can be rewritten as -1/2.
2. Combine the fractions:
(3x-2)/(8) + -(x-2)/(4) - 1/2 = 0
3. Find a common denominator:
The least common multiple of 8, 4, and 2 is 8. So, we need to multiply the numerators and denominators accordingly.
(3x-2)/(8) + -(x-2)/(4) - 1/2 = [(3x-2)(1) + -(x-2)(2) - 1(4)]/8
4. Distribute and simplify:
(3x-2)/(8) + -(x-2)/(4) - 1/2 = (3x-2 - 2(x-2) - 4)/8
= (3x-2 - 2x+4 - 4)/8
= (x-2)/8
5. Set the numerator equal to 0:
(x-2)/8 = 0
6. Solve for x:
Multiply both sides of the equation by 8 to isolate (x-2):
x-2 = 0
Add 2 to both sides of the equation to solve for x:
x = 2
Therefore, the solution to the equation is x = 2.