Solve 3d-1/2(2d-4)=-3/4(d+4)

$$3 d - \frac { 1 } { 2 } ( 2 d - 4 ) = - \frac { 3 } { 4 } ( d + 4 )$$

Solve for d

$$d = -\frac{20}{11} = -1\frac{9}{11} \approx -1.818181818$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{2} by 2d-4.

$$3d-\frac{1}{2}\times 2d-\frac{1}{2}\left(-4\right)=-\frac{3}{4}\left(d+4\right)$$

Cancel out 2 and 2.

$$3d-d-\frac{1}{2}\left(-4\right)=-\frac{3}{4}\left(d+4\right)$$

Express -\frac{1}{2}\left(-4\right) as a single fraction.

$$3d-d+\frac{-\left(-4\right)}{2}=-\frac{3}{4}\left(d+4\right)$$

Multiply -1 and -4 to get 4.

$$3d-d+\frac{4}{2}=-\frac{3}{4}\left(d+4\right)$$

Divide 4 by 2 to get 2.

$$3d-d+2=-\frac{3}{4}\left(d+4\right)$$

Combine 3d and -d to get 2d.

$$2d+2=-\frac{3}{4}\left(d+4\right)$$

Use the distributive property to multiply -\frac{3}{4} by d+4.

$$2d+2=-\frac{3}{4}d-\frac{3}{4}\times 4$$

Cancel out 4 and 4.

$$2d+2=-\frac{3}{4}d-3$$

Add \frac{3}{4}d to both sides.

$$2d+2+\frac{3}{4}d=-3$$

Combine 2d and \frac{3}{4}d to get \frac{11}{4}d.

$$\frac{11}{4}d+2=-3$$

Subtract 2 from both sides.

$$\frac{11}{4}d=-3-2$$

Subtract 2 from -3 to get -5.

$$\frac{11}{4}d=-5$$

Multiply both sides by \frac{4}{11}, the reciprocal of \frac{11}{4}.

$$d=-5\times \frac{4}{11}$$

Express -5\times \frac{4}{11} as a single fraction.

$$d=\frac{-5\times 4}{11}$$

Multiply -5 and 4 to get -20.

$$d=\frac{-20}{11}$$

Fraction \frac{-20}{11} can be rewritten as -\frac{20}{11} by extracting the negative sign.

$$d=-\frac{20}{11}$$