Solve 2(2x+3)/5+4/5x=3(x-2)/2-5x-6/10

$$\frac { 2 ( 2 x + 3 ) } { 5 } + \frac { 4 } { 5 } x = \frac { 3 ( x - 2 ) } { 2 } - \frac { 5 x - 6 } { 10 }$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

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

$$2\times 2\left(2x+3\right)+8x=5\times 3\left(x-2\right)-\left(5x-6\right)$$

Multiply 2 and 2 to get 4.

$$4\left(2x+3\right)+8x=5\times 3\left(x-2\right)-\left(5x-6\right)$$

Use the distributive property to multiply 4 by 2x+3.

$$8x+12+8x=5\times 3\left(x-2\right)-\left(5x-6\right)$$

Combine 8x and 8x to get 16x.

$$16x+12=5\times 3\left(x-2\right)-\left(5x-6\right)$$

Multiply 5 and 3 to get 15.

$$16x+12=15\left(x-2\right)-\left(5x-6\right)$$

Use the distributive property to multiply 15 by x-2.

$$16x+12=15x-30-\left(5x-6\right)$$

To find the opposite of 5x-6, find the opposite of each term.

$$16x+12=15x-30-5x-\left(-6\right)$$

The opposite of -6 is 6.

$$16x+12=15x-30-5x+6$$

Combine 15x and -5x to get 10x.

$$16x+12=10x-30+6$$

Add -30 and 6 to get -24.

$$16x+12=10x-24$$

Subtract 10x from both sides.

$$16x+12-10x=-24$$

Combine 16x and -10x to get 6x.

$$6x+12=-24$$

Subtract 12 from both sides.

$$6x=-24-12$$

Subtract 12 from -24 to get -36.

$$6x=-36$$

Divide both sides by 6.

$$x=\frac{-36}{6}$$

Divide -36 by 6 to get -6.

$$x=-6$$