Solve 2(x-1)/3-3(4x-1)/5=5(3x-2)/2-32

$$\frac { 2 ( x - 1 ) } { 3 } - \frac { 3 ( 4 x - 1 ) } { 5 } = \frac { 5 ( 3 x - 2 ) } { 2 } - 32$$

Solve for x

$$x=4$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,5,2.

$$10\times 2\left(x-1\right)-6\times 3\left(4x-1\right)=15\times 5\left(3x-2\right)-960$$

Multiply 10 and 2 to get 20.

$$20\left(x-1\right)-6\times 3\left(4x-1\right)=15\times 5\left(3x-2\right)-960$$

Use the distributive property to multiply 20 by x-1.

$$20x-20-6\times 3\left(4x-1\right)=15\times 5\left(3x-2\right)-960$$

Multiply -6 and 3 to get -18.

$$20x-20-18\left(4x-1\right)=15\times 5\left(3x-2\right)-960$$

Use the distributive property to multiply -18 by 4x-1.

$$20x-20-72x+18=15\times 5\left(3x-2\right)-960$$

Combine 20x and -72x to get -52x.

$$-52x-20+18=15\times 5\left(3x-2\right)-960$$

Add -20 and 18 to get -2.

$$-52x-2=15\times 5\left(3x-2\right)-960$$

Multiply 15 and 5 to get 75.

$$-52x-2=75\left(3x-2\right)-960$$

Use the distributive property to multiply 75 by 3x-2.

$$-52x-2=225x-150-960$$

Subtract 960 from -150 to get -1110.

$$-52x-2=225x-1110$$

Subtract 225x from both sides.

$$-52x-2-225x=-1110$$

Combine -52x and -225x to get -277x.

$$-277x-2=-1110$$

Add 2 to both sides.

$$-277x=-1110+2$$

Add -1110 and 2 to get -1108.

$$-277x=-1108$$

Divide both sides by -277.

$$x=\frac{-1108}{-277}$$

Divide -1108 by -277 to get 4.

$$x=4$$