Solve 14:1/2-2(x+3)/5=3x/2-2(x-7)/3

$$14 : \frac { 1 } { 2 } - \frac { 2 ( x + 3 ) } { 5 } = \frac { 3 x } { 2 } - \frac { 2 ( x - 7 ) } { 3 }$$

Solve for x

$$x = \frac{664}{37} = 17\frac{35}{37} \approx 17.945945946$$

Steps for Solving Linear Equation

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

$$30\times \frac{14}{\frac{1}{2}}-6\times 2\left(x+3\right)=15\times 3x-10\times 2\left(x-7\right)$$

Divide 14 by \frac{1}{2} by multiplying 14 by the reciprocal of \frac{1}{2}.

$$30\times 14\times 2-6\times 2\left(x+3\right)=15\times 3x-10\times 2\left(x-7\right)$$

Multiply 14 and 2 to get 28.

$$30\times 28-6\times 2\left(x+3\right)=15\times 3x-10\times 2\left(x-7\right)$$

Multiply 30 and 28 to get 840.

$$840-6\times 2\left(x+3\right)=15\times 3x-10\times 2\left(x-7\right)$$

Multiply -6 and 2 to get -12.

$$840-12\left(x+3\right)=15\times 3x-10\times 2\left(x-7\right)$$

Use the distributive property to multiply -12 by x+3.

$$840-12x-36=15\times 3x-10\times 2\left(x-7\right)$$

Subtract 36 from 840 to get 804.

$$804-12x=15\times 3x-10\times 2\left(x-7\right)$$

Multiply 15 and 3 to get 45. Multiply -10 and 2 to get -20.

$$804-12x=45x-20\left(x-7\right)$$

Use the distributive property to multiply -20 by x-7.

$$804-12x=45x-20x+140$$

Combine 45x and -20x to get 25x.

$$804-12x=25x+140$$

Subtract 25x from both sides.

$$804-12x-25x=140$$

Combine -12x and -25x to get -37x.

$$804-37x=140$$

Subtract 804 from both sides.

$$-37x=140-804$$

Subtract 804 from 140 to get -664.

$$-37x=-664$$

Divide both sides by -37.

$$x=\frac{-664}{-37}$$

Fraction \frac{-664}{-37} can be simplified to \frac{664}{37} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{664}{37}$$