Final answer:
To solve the equation 1/4(5x+16/3)-2/4(3/4x+1/2)=-5, distribute the fractions, combine the like terms, isolate x, and perform the necessary operations.
Step-by-step explanation:
To solve the equation 1/4(5x+16/3)-2/4(3/4x+1/2)=-5, we need to simplify and solve for x step-by-step.
- Distribute the 1/4 to the terms inside the first parentheses: (1/4)(5x+16/3)=5/4x+4/3
- Distribute the -2/4 to the terms inside the second parentheses: (-2/4)(3/4x+1/2)=-3/4x-1/2
- Combine like terms on each side of the equation: (5/4x+4/3)-(-3/4x-1/2)=-5
Simplifying further, we have 5/4x+4/3+3/4x+1/2=-5 - Combine like terms again: 5/4x+3/4x+4/3+1/2=-5
Simplifying further, we have 8/4x+(8/3+6/6)=-5 - Add the fractions: 8/4x+14/6=-5
Simplifying further, we have 8/4x+7/3=-5 - Subtract 7/3 from both sides of the equation: 8/4x=-5-7/3
Simplifying further, we have 8/4x=-15/3-7/3 - Combine the fractions: 8/4x=-22/3
- Divide both sides of the equation by 8/4 to isolate x: x=(-22/3)/(8/4)
- Simplify by multiplying the numerator and denominator of the right side of the equation by the reciprocal of 8/4: x=(-22/3)(4/8)
- Perform the multiplication and simplify the fraction: x=(-2*11)/(1*3)
Therefore, the solution to the equation is x=-22/3