Solve 4(3x-7)/5-7x-3/2+x/10=3(4-5x)

$$\frac { 4 ( 3 x - 7 ) } { 5 } - \frac { 7 x - 3 } { 2 } + \frac { x } { 10 } = 3 ( 4 - 5 x )$$

Solve for x

$$x = \frac{23}{20} = 1\frac{3}{20} = 1.15$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 10, the least common multiple of 5,2,10.

$$2\times 4\left(3x-7\right)-5\left(7x-3\right)+x=30\left(4-5x\right)$$

Multiply 2 and 4 to get 8.

$$8\left(3x-7\right)-5\left(7x-3\right)+x=30\left(4-5x\right)$$

Use the distributive property to multiply 8 by 3x-7.

$$24x-56-5\left(7x-3\right)+x=30\left(4-5x\right)$$

Use the distributive property to multiply -5 by 7x-3.

$$24x-56-35x+15+x=30\left(4-5x\right)$$

Combine 24x and -35x to get -11x.

$$-11x-56+15+x=30\left(4-5x\right)$$

Add -56 and 15 to get -41.

$$-11x-41+x=30\left(4-5x\right)$$

Combine -11x and x to get -10x.

$$-10x-41=30\left(4-5x\right)$$

Use the distributive property to multiply 30 by 4-5x.

$$-10x-41=120-150x$$

Add 150x to both sides.

$$-10x-41+150x=120$$

Combine -10x and 150x to get 140x.

$$140x-41=120$$

Add 41 to both sides.

$$140x=120+41$$

Add 120 and 41 to get 161.

$$140x=161$$

Divide both sides by 140.

$$x=\frac{161}{140}$$

Reduce the fraction \frac{161}{140} to lowest terms by extracting and canceling out 7.

$$x=\frac{23}{20}$$