Solve 7(x+4)-2[x-3(5+x)]=2/3(x-6)

$$7 ( x + 4 ) - 2 [ x - 3 ( 5 + x ) ] = \frac { 2 } { 3 } ( x - 6 )$$

Solve for x

$$x=-6$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by x+4.

$$7x+28-2\left(x-3\left(5+x\right)\right)=\frac{2}{3}\left(x-6\right)$$

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

$$7x+28-2\left(x-15-3x\right)=\frac{2}{3}\left(x-6\right)$$

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

$$7x+28-2\left(-2x-15\right)=\frac{2}{3}\left(x-6\right)$$

Use the distributive property to multiply -2 by -2x-15.

$$7x+28+4x+30=\frac{2}{3}\left(x-6\right)$$

Combine 7x and 4x to get 11x.

$$11x+28+30=\frac{2}{3}\left(x-6\right)$$

Add 28 and 30 to get 58.

$$11x+58=\frac{2}{3}\left(x-6\right)$$

Use the distributive property to multiply \frac{2}{3} by x-6.

$$11x+58=\frac{2}{3}x+\frac{2}{3}\left(-6\right)$$

Express \frac{2}{3}\left(-6\right) as a single fraction.

$$11x+58=\frac{2}{3}x+\frac{2\left(-6\right)}{3}$$

Multiply 2 and -6 to get -12.

$$11x+58=\frac{2}{3}x+\frac{-12}{3}$$

Divide -12 by 3 to get -4.

$$11x+58=\frac{2}{3}x-4$$

Subtract \frac{2}{3}x from both sides.

$$11x+58-\frac{2}{3}x=-4$$

Combine 11x and -\frac{2}{3}x to get \frac{31}{3}x.

$$\frac{31}{3}x+58=-4$$

Subtract 58 from both sides.

$$\frac{31}{3}x=-4-58$$

Subtract 58 from -4 to get -62.

$$\frac{31}{3}x=-62$$

Multiply both sides by \frac{3}{31}, the reciprocal of \frac{31}{3}.

$$x=-62\times \frac{3}{31}$$

Express -62\times \frac{3}{31} as a single fraction.

$$x=\frac{-62\times 3}{31}$$

Multiply -62 and 3 to get -186.

$$x=\frac{-186}{31}$$

Divide -186 by 31 to get -6.

$$x=-6$$