Solve 3(x-3)/4+4x-10*5/10=3(x+1)/5+6

$$\frac { 3 ( x - 3 ) } { 4 } + \frac { 4 x - 10 \cdot 5 } { 10 } = \frac { 3 ( x + 1 ) } { 5 } + 6$$

Solve for x

$$x = \frac{277}{11} = 25\frac{2}{11} \approx 25.181818182$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 4,10,5.

$$5\times 3\left(x-3\right)+2\left(4x-10\times 5\right)=4\times 3\left(x+1\right)+120$$

Multiply 5 and 3 to get 15.

$$15\left(x-3\right)+2\left(4x-10\times 5\right)=4\times 3\left(x+1\right)+120$$

Use the distributive property to multiply 15 by x-3.

$$15x-45+2\left(4x-10\times 5\right)=4\times 3\left(x+1\right)+120$$

Multiply 10 and 5 to get 50.

$$15x-45+2\left(4x-50\right)=4\times 3\left(x+1\right)+120$$

Use the distributive property to multiply 2 by 4x-50.

$$15x-45+8x-100=4\times 3\left(x+1\right)+120$$

Combine 15x and 8x to get 23x.

$$23x-45-100=4\times 3\left(x+1\right)+120$$

Subtract 100 from -45 to get -145.

$$23x-145=4\times 3\left(x+1\right)+120$$

Multiply 4 and 3 to get 12.

$$23x-145=12\left(x+1\right)+120$$

Use the distributive property to multiply 12 by x+1.

$$23x-145=12x+12+120$$

Add 12 and 120 to get 132.

$$23x-145=12x+132$$

Subtract 12x from both sides.

$$23x-145-12x=132$$

Combine 23x and -12x to get 11x.

$$11x-145=132$$

Add 145 to both sides.

$$11x=132+145$$

Add 132 and 145 to get 277.

$$11x=277$$

Divide both sides by 11.

$$x=\frac{277}{11}$$