Solve 2left(x-5right)/3-2x+3/5=1/3x+2left(-x-25right)/15

$$\frac{ 2 \left( x-5 \right) }{ 3 } - \frac{ 2x+3 }{ 5 } = \frac{ 1 }{ 3 } x+ \frac{ 2 \left( -x-25 \right) }{ 15 }$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 3,5,15.

$$5\times 2\left(x-5\right)-3\left(2x+3\right)=5x+2\left(-x-25\right)$$

Multiply 5 and 2 to get 10.

$$10\left(x-5\right)-3\left(2x+3\right)=5x+2\left(-x-25\right)$$

Use the distributive property to multiply 10 by x-5.

$$10x-50-3\left(2x+3\right)=5x+2\left(-x-25\right)$$

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

$$10x-50-6x-9=5x+2\left(-x-25\right)$$

Combine 10x and -6x to get 4x.

$$4x-50-9=5x+2\left(-x-25\right)$$

Subtract 9 from -50 to get -59.

$$4x-59=5x+2\left(-x-25\right)$$

Use the distributive property to multiply 2 by -x-25.

$$4x-59=5x+2\left(-x\right)-50$$

Subtract 5x from both sides.

$$4x-59-5x=2\left(-x\right)-50$$

Combine 4x and -5x to get -x.

$$-x-59=2\left(-x\right)-50$$

Subtract 2\left(-x\right) from both sides.

$$-x-59-2\left(-x\right)=-50$$

Multiply -1 and 2 to get -2.

$$-x-59-2\left(-1\right)x=-50$$

Multiply -2 and -1 to get 2.

$$-x-59+2x=-50$$

Combine -x and 2x to get x.

$$x-59=-50$$

Add 59 to both sides.

$$x=-50+59$$

Add -50 and 59 to get 9.

$$x=9$$