Solve -3(x-5)-2(x+7)=4(x+12)

$$- 3 ( x - 5 ) - 2 ( x + 7 ) = 4 ( x + 12 )$$

Solve for x

$$x = -\frac{47}{9} = -5\frac{2}{9} \approx -5.222222222$$

Steps for Solving Linear Equation

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

$$-3x+15-2\left(x+7\right)=4\left(x+12\right)$$

Use the distributive property to multiply -2 by x+7.

$$-3x+15-2x-14=4\left(x+12\right)$$

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

$$-5x+15-14=4\left(x+12\right)$$

Subtract 14 from 15 to get 1.

$$-5x+1=4\left(x+12\right)$$

Use the distributive property to multiply 4 by x+12.

$$-5x+1=4x+48$$

Subtract 4x from both sides.

$$-5x+1-4x=48$$

Combine -5x and -4x to get -9x.

$$-9x+1=48$$

Subtract 1 from both sides.

$$-9x=48-1$$

Subtract 1 from 48 to get 47.

$$-9x=47$$

Divide both sides by -9.

$$x=\frac{47}{-9}$$

Fraction \frac{47}{-9} can be rewritten as -\frac{47}{9} by extracting the negative sign.

$$x=-\frac{47}{9}$$