Solve 3(x+1)-5(x+10)=9(x-4)-9(x-8)

$$3 ( x + 1 ) - 5 ( x + 10 ) = 9 ( x - 4 ) - 9 ( x - 8 )$$

Solve for x

$$x = -\frac{83}{2} = -41\frac{1}{2} = -41.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by x+1.

$$3x+3-5\left(x+10\right)=9\left(x-4\right)-9\left(x-8\right)$$

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

$$3x+3-5x-50=9\left(x-4\right)-9\left(x-8\right)$$

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

$$-2x+3-50=9\left(x-4\right)-9\left(x-8\right)$$

Subtract 50 from 3 to get -47.

$$-2x-47=9\left(x-4\right)-9\left(x-8\right)$$

Use the distributive property to multiply 9 by x-4.

$$-2x-47=9x-36-9\left(x-8\right)$$

Use the distributive property to multiply -9 by x-8.

$$-2x-47=9x-36-9x+72$$

Combine 9x and -9x to get 0.

$$-2x-47=-36+72$$

Add -36 and 72 to get 36.

$$-2x-47=36$$

Add 47 to both sides.

$$-2x=36+47$$

Add 36 and 47 to get 83.

$$-2x=83$$

Divide both sides by -2.

$$x=\frac{83}{-2}$$

Fraction \frac{83}{-2} can be rewritten as -\frac{83}{2} by extracting the negative sign.

$$x=-\frac{83}{2}$$