Solve x+4/3-2/3=4/5-32/10x

$$\frac { x + 4 } { 3 } - \frac { 2 } { 3 } = \frac { 4 } { 5 } - 3 \frac { 2 } { 10 } x$$

Solve for x

$$x=\frac{2}{53}\approx 0.037735849$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 3,5,10.

$$10\left(x+4\right)-20=24-3\left(3\times 10+2\right)x$$

Use the distributive property to multiply 10 by x+4.

$$10x+40-20=24-3\left(3\times 10+2\right)x$$

Subtract 20 from 40 to get 20.

$$10x+20=24-3\left(3\times 10+2\right)x$$

Multiply 3 and 10 to get 30.

$$10x+20=24-3\left(30+2\right)x$$

Add 30 and 2 to get 32.

$$10x+20=24-3\times 32x$$

Multiply 3 and 32 to get 96.

$$10x+20=24-96x$$

Add 96x to both sides.

$$10x+20+96x=24$$

Combine 10x and 96x to get 106x.

$$106x+20=24$$

Subtract 20 from both sides.

$$106x=24-20$$

Subtract 20 from 24 to get 4.

$$106x=4$$

Divide both sides by 106.

$$x=\frac{4}{106}$$

Reduce the fraction \frac{4}{106} to lowest terms by extracting and canceling out 2.

$$x=\frac{2}{53}$$