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

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

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$6\left(x-\frac{5}{3}\left(x+4\right)\right)=5\left(x-3\right)-10\left(x+2\right)$$

Use the distributive property to multiply -\frac{5}{3} by x+4.

$$6\left(x-\frac{5}{3}x-\frac{5}{3}\times 4\right)=5\left(x-3\right)-10\left(x+2\right)$$

Express -\frac{5}{3}\times 4 as a single fraction.

$$6\left(x-\frac{5}{3}x+\frac{-5\times 4}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Multiply -5 and 4 to get -20.

$$6\left(x-\frac{5}{3}x+\frac{-20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$6\left(x-\frac{5}{3}x-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Combine x and -\frac{5}{3}x to get -\frac{2}{3}x.

$$6\left(-\frac{2}{3}x-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Use the distributive property to multiply 6 by -\frac{2}{3}x-\frac{20}{3}.

$$6\left(-\frac{2}{3}\right)x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

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

$$\frac{6\left(-2\right)}{3}x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Multiply 6 and -2 to get -12.

$$\frac{-12}{3}x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Divide -12 by 3 to get -4.

$$-4x+6\left(-\frac{20}{3}\right)=5\left(x-3\right)-10\left(x+2\right)$$

Express 6\left(-\frac{20}{3}\right) as a single fraction.

$$-4x+\frac{6\left(-20\right)}{3}=5\left(x-3\right)-10\left(x+2\right)$$

Multiply 6 and -20 to get -120.

$$-4x+\frac{-120}{3}=5\left(x-3\right)-10\left(x+2\right)$$

Divide -120 by 3 to get -40.

$$-4x-40=5\left(x-3\right)-10\left(x+2\right)$$

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

$$-4x-40=5x-15-10\left(x+2\right)$$

Use the distributive property to multiply -10 by x+2.

$$-4x-40=5x-15-10x-20$$

Combine 5x and -10x to get -5x.

$$-4x-40=-5x-15-20$$

Subtract 20 from -15 to get -35.

$$-4x-40=-5x-35$$

Add 5x to both sides.

$$-4x-40+5x=-35$$

Combine -4x and 5x to get x.

$$x-40=-35$$

Add 40 to both sides.

$$x=-35+40$$

Add -35 and 40 to get 5.

$$x=5$$