Solve 1/10(x+51)=-2(6-x)

$$\frac { 1 } { 10 } ( x + 51 ) = - 2 ( 6 - x )$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{10} by x+51.

$$\frac{1}{10}x+\frac{1}{10}\times 51=-2\left(6-x\right)$$

Multiply \frac{1}{10} and 51 to get \frac{51}{10}.

$$\frac{1}{10}x+\frac{51}{10}=-2\left(6-x\right)$$

Use the distributive property to multiply -2 by 6-x.

$$\frac{1}{10}x+\frac{51}{10}=-12+2x$$

Subtract 2x from both sides.

$$\frac{1}{10}x+\frac{51}{10}-2x=-12$$

Combine \frac{1}{10}x and -2x to get -\frac{19}{10}x.

$$-\frac{19}{10}x+\frac{51}{10}=-12$$

Subtract \frac{51}{10} from both sides.

$$-\frac{19}{10}x=-12-\frac{51}{10}$$

Convert -12 to fraction -\frac{120}{10}.

$$-\frac{19}{10}x=-\frac{120}{10}-\frac{51}{10}$$

Since -\frac{120}{10} and \frac{51}{10} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{19}{10}x=\frac{-120-51}{10}$$

Subtract 51 from -120 to get -171.

$$-\frac{19}{10}x=-\frac{171}{10}$$

Multiply both sides by -\frac{10}{19}, the reciprocal of -\frac{19}{10}.

$$x=-\frac{171}{10}\left(-\frac{10}{19}\right)$$

Multiply -\frac{171}{10} times -\frac{10}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-171\left(-10\right)}{10\times 19}$$

Do the multiplications in the fraction \frac{-171\left(-10\right)}{10\times 19}.

$$x=\frac{1710}{190}$$

Divide 1710 by 190 to get 9.

$$x=9$$