Solve 1/9[3x-6-5(7x/2-5)]+13(x-5)+1/4=0

$$\frac { 1 } { 9 } [ 3 x - 6 - 5 ( \frac { 7 x } { 2 } - 5 ) ] + 13 ( x - 5 ) + \frac { 1 } { 4 } = 0$$

Solve for x

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 36, the least common multiple of 9,2,4.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468\left(x-5\right)+9=0$$

Use the distributive property to multiply 468 by x-5.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x-2340+9=0$$

Add -2340 and 9 to get -2331.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x-2331=0$$

Add 2331 to both sides. Anything plus zero gives itself.

$$4\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+468x=2331$$

Multiply both sides of the equation by 2.

$$8\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+936x=4662$$

Multiply both sides of the equation by 2.

$$16\left(3x-6-5\left(\frac{7x}{2}-5\right)\right)+1872x=9324$$

Use the distributive property to multiply -5 by \frac{7x}{2}-5.

$$16\left(3x-6-5\times \frac{7x}{2}+25\right)+1872x=9324$$

Express -5\times \frac{7x}{2} as a single fraction.

$$16\left(3x-6+\frac{-5\times 7x}{2}+25\right)+1872x=9324$$

Multiply -5 and 7 to get -35.

$$16\left(3x-6+\frac{-35x}{2}+25\right)+1872x=9324$$

Add -6 and 25 to get 19.

$$16\left(3x+19+\frac{-35x}{2}\right)+1872x=9324$$

Use the distributive property to multiply 16 by 3x+19+\frac{-35x}{2}.

$$48x+304+16\times \frac{-35x}{2}+1872x=9324$$

Cancel out 2, the greatest common factor in 16 and 2.

$$48x+304+8\left(-35\right)x+1872x=9324$$

Multiply 8 and -35 to get -280.

$$48x+304-280x+1872x=9324$$

Combine 48x and -280x to get -232x.

$$-232x+304+1872x=9324$$

Combine -232x and 1872x to get 1640x.

$$1640x+304=9324$$

Subtract 304 from both sides.

$$1640x=9324-304$$

Subtract 304 from 9324 to get 9020.

$$1640x=9020$$

Divide both sides by 1640.

$$x=\frac{9020}{1640}$$

Reduce the fraction \frac{9020}{1640} to lowest terms by extracting and canceling out 820.

$$x=\frac{11}{2}$$