Solve 4x+1/2-2x+3/4=x-4

$$\frac { 4 x + 1 } { 2 } - \frac { 2 x + 3 } { 4 } = x - 4$$

Solve for x

$$x = -\frac{15}{2} = -7\frac{1}{2} = -7.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$2\left(4x+1\right)-\left(2x+3\right)=4x-16$$

Use the distributive property to multiply 2 by 4x+1.

$$8x+2-\left(2x+3\right)=4x-16$$

To find the opposite of 2x+3, find the opposite of each term.

$$8x+2-2x-3=4x-16$$

Combine 8x and -2x to get 6x.

$$6x+2-3=4x-16$$

Subtract 3 from 2 to get -1.

$$6x-1=4x-16$$

Subtract 4x from both sides.

$$6x-1-4x=-16$$

Combine 6x and -4x to get 2x.

$$2x-1=-16$$

Add 1 to both sides.

$$2x=-16+1$$

Add -16 and 1 to get -15.

$$2x=-15$$

Divide both sides by 2.

$$x=\frac{-15}{2}$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$x=-\frac{15}{2}$$