Solve 1/2(4x+4)-31/4=6(21/4x+5)+9

$$\frac { 1 } { 2 } ( 4 x + 4 ) - 3 \frac { 1 } { 4 } = 6 ( 2 \frac { 1 } { 4 } x + 5 ) + 9$$

Solve for x

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Steps for Solving Linear Equation

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

$$2\left(4x+4\right)-\left(3\times 4+1\right)=24\left(\frac{2\times 4+1}{4}x+5\right)+36$$

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

$$8x+8-\left(3\times 4+1\right)=24\left(\frac{2\times 4+1}{4}x+5\right)+36$$

Multiply 3 and 4 to get 12.

$$8x+8-\left(12+1\right)=24\left(\frac{2\times 4+1}{4}x+5\right)+36$$

Add 12 and 1 to get 13.

$$8x+8-13=24\left(\frac{2\times 4+1}{4}x+5\right)+36$$

Subtract 13 from 8 to get -5.

$$8x-5=24\left(\frac{2\times 4+1}{4}x+5\right)+36$$

Multiply 2 and 4 to get 8.

$$8x-5=24\left(\frac{8+1}{4}x+5\right)+36$$

Add 8 and 1 to get 9.

$$8x-5=24\left(\frac{9}{4}x+5\right)+36$$

Use the distributive property to multiply 24 by \frac{9}{4}x+5.

$$8x-5=24\times \frac{9}{4}x+120+36$$

Express 24\times \frac{9}{4} as a single fraction.

$$8x-5=\frac{24\times 9}{4}x+120+36$$

Multiply 24 and 9 to get 216.

$$8x-5=\frac{216}{4}x+120+36$$

Divide 216 by 4 to get 54.

$$8x-5=54x+120+36$$

Add 120 and 36 to get 156.

$$8x-5=54x+156$$

Subtract 54x from both sides.

$$8x-5-54x=156$$

Combine 8x and -54x to get -46x.

$$-46x-5=156$$

Add 5 to both sides.

$$-46x=156+5$$

Add 156 and 5 to get 161.

$$-46x=161$$

Divide both sides by -46.

$$x=\frac{161}{-46}$$

Reduce the fraction \frac{161}{-46} to lowest terms by extracting and canceling out 23.

$$x=-\frac{7}{2}$$