Solve 3/4(x-8)-4x=2(x-3)-1/2x

$$\frac { 3 } { 4 } ( x - 8 ) - 4 x = 2 ( x - 3 ) - \frac { 1 } { 2 } x$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{4} by x-8.

$$\frac{3}{4}x+\frac{3}{4}\left(-8\right)-4x=2\left(x-3\right)-\frac{1}{2}x$$

Express \frac{3}{4}\left(-8\right) as a single fraction.

$$\frac{3}{4}x+\frac{3\left(-8\right)}{4}-4x=2\left(x-3\right)-\frac{1}{2}x$$

Multiply 3 and -8 to get -24.

$$\frac{3}{4}x+\frac{-24}{4}-4x=2\left(x-3\right)-\frac{1}{2}x$$

Divide -24 by 4 to get -6.

$$\frac{3}{4}x-6-4x=2\left(x-3\right)-\frac{1}{2}x$$

Combine \frac{3}{4}x and -4x to get -\frac{13}{4}x.

$$-\frac{13}{4}x-6=2\left(x-3\right)-\frac{1}{2}x$$

Use the distributive property to multiply 2 by x-3.

$$-\frac{13}{4}x-6=2x-6-\frac{1}{2}x$$

Combine 2x and -\frac{1}{2}x to get \frac{3}{2}x.

$$-\frac{13}{4}x-6=\frac{3}{2}x-6$$

Subtract \frac{3}{2}x from both sides.

$$-\frac{13}{4}x-6-\frac{3}{2}x=-6$$

Combine -\frac{13}{4}x and -\frac{3}{2}x to get -\frac{19}{4}x.

$$-\frac{19}{4}x-6=-6$$

Add 6 to both sides.

$$-\frac{19}{4}x=-6+6$$

Add -6 and 6 to get 0.

$$-\frac{19}{4}x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -\frac{19}{4} is not equal to 0, x must be equal to 0.

$$x=0$$