Solve 3(2-5x)-2(5x-3)+2x=1-2(3-2x)

$$3 ( 2 - 5 x ) - 2 ( 5 x - 3 ) + 2 x = 1 - 2 ( 3 - 2 x )$$

Solve for x

$$x=\frac{17}{27}\approx 0.62962963$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2-5x.

$$6-15x-2\left(5x-3\right)+2x=1-2\left(3-2x\right)$$

Use the distributive property to multiply -2 by 5x-3.

$$6-15x-10x+6+2x=1-2\left(3-2x\right)$$

Combine -15x and -10x to get -25x.

$$6-25x+6+2x=1-2\left(3-2x\right)$$

Add 6 and 6 to get 12.

$$12-25x+2x=1-2\left(3-2x\right)$$

Combine -25x and 2x to get -23x.

$$12-23x=1-2\left(3-2x\right)$$

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

$$12-23x=1-6+4x$$

Subtract 6 from 1 to get -5.

$$12-23x=-5+4x$$

Subtract 4x from both sides.

$$12-23x-4x=-5$$

Combine -23x and -4x to get -27x.

$$12-27x=-5$$

Subtract 12 from both sides.

$$-27x=-5-12$$

Subtract 12 from -5 to get -17.

$$-27x=-17$$

Divide both sides by -27.

$$x=\frac{-17}{-27}$$

Fraction \frac{-17}{-27} can be simplified to \frac{17}{27} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{17}{27}$$