Solve x-(2x-(3x-4)/7)=4x-27/3-3

$$x - ( 2 x - \frac { ( 3 x - 4 ) } { 7 } ) = \frac { 4 x - 27 } { 3 } - 3$$

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 21, the least common multiple of 7,3.

$$21x-21\left(2x-\frac{3x-4}{7}\right)=7\left(4x-27\right)-63$$

Use the distributive property to multiply 7 by 4x-27.

$$21x-21\left(2x-\frac{3x-4}{7}\right)=28x-189-63$$

Subtract 63 from -189 to get -252.

$$21x-21\left(2x-\frac{3x-4}{7}\right)=28x-252$$

Divide each term of 3x-4 by 7 to get \frac{3}{7}x-\frac{4}{7}.

$$21x-21\left(2x-\left(\frac{3}{7}x-\frac{4}{7}\right)\right)=28x-252$$

To find the opposite of \frac{3}{7}x-\frac{4}{7}, find the opposite of each term.

$$21x-21\left(2x-\frac{3}{7}x-\left(-\frac{4}{7}\right)\right)=28x-252$$

The opposite of -\frac{4}{7} is \frac{4}{7}.

$$21x-21\left(2x-\frac{3}{7}x+\frac{4}{7}\right)=28x-252$$

Combine 2x and -\frac{3}{7}x to get \frac{11}{7}x.

$$21x-21\left(\frac{11}{7}x+\frac{4}{7}\right)=28x-252$$

Use the distributive property to multiply -21 by \frac{11}{7}x+\frac{4}{7}.

$$21x-21\times \frac{11}{7}x-21\times \frac{4}{7}=28x-252$$

Express -21\times \frac{11}{7} as a single fraction.

$$21x+\frac{-21\times 11}{7}x-21\times \frac{4}{7}=28x-252$$

Multiply -21 and 11 to get -231.

$$21x+\frac{-231}{7}x-21\times \frac{4}{7}=28x-252$$

Divide -231 by 7 to get -33.

$$21x-33x-21\times \frac{4}{7}=28x-252$$

Express -21\times \frac{4}{7} as a single fraction.

$$21x-33x+\frac{-21\times 4}{7}=28x-252$$

Multiply -21 and 4 to get -84.

$$21x-33x+\frac{-84}{7}=28x-252$$

Divide -84 by 7 to get -12.

$$21x-33x-12=28x-252$$

Combine 21x and -33x to get -12x.

$$-12x-12=28x-252$$

Subtract 28x from both sides.

$$-12x-12-28x=-252$$

Combine -12x and -28x to get -40x.

$$-40x-12=-252$$

Add 12 to both sides.

$$-40x=-252+12$$

Add -252 and 12 to get -240.

$$-40x=-240$$

Divide both sides by -40.

$$x=\frac{-240}{-40}$$

Divide -240 by -40 to get 6.

$$x=6$$