Solve 6-4(x-3)=3x-5(x-5)

$$6-4(x-3)=3x-5(x-5)$$

Solve for x

$$x = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply -4 by x-3.

$$6-4x+12=3x-5\left(x-5\right)$$

Add 6 and 12 to get 18.

$$18-4x=3x-5\left(x-5\right)$$

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

$$18-4x=3x-5x+25$$

Combine 3x and -5x to get -2x.

$$18-4x=-2x+25$$

Add 2x to both sides.

$$18-4x+2x=25$$

Combine -4x and 2x to get -2x.

$$18-2x=25$$

Subtract 18 from both sides.

$$-2x=25-18$$

Subtract 18 from 25 to get 7.

$$-2x=7$$

Divide both sides by -2.

$$x=\frac{7}{-2}$$

Fraction \frac{7}{-2} can be rewritten as -\frac{7}{2} by extracting the negative sign.

$$x=-\frac{7}{2}$$