Solve 6x+4/5-9(x-3)/2=5x+4/3

$$\frac { 6 x + 4 } { 5 } - \frac { 9 ( x - 3 ) } { 2 } = \frac { 5 x + 4 } { 3 }$$

Solve for x

$$x = \frac{389}{149} = 2\frac{91}{149} \approx 2.610738255$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 30, the least common multiple of 5,2,3.

$$6\left(6x+4\right)-15\times 9\left(x-3\right)=10\left(5x+4\right)$$

Use the distributive property to multiply 6 by 6x+4.

$$36x+24-15\times 9\left(x-3\right)=10\left(5x+4\right)$$

Multiply -15 and 9 to get -135.

$$36x+24-135\left(x-3\right)=10\left(5x+4\right)$$

Use the distributive property to multiply -135 by x-3.

$$36x+24-135x+405=10\left(5x+4\right)$$

Combine 36x and -135x to get -99x.

$$-99x+24+405=10\left(5x+4\right)$$

Add 24 and 405 to get 429.

$$-99x+429=10\left(5x+4\right)$$

Use the distributive property to multiply 10 by 5x+4.

$$-99x+429=50x+40$$

Subtract 50x from both sides.

$$-99x+429-50x=40$$

Combine -99x and -50x to get -149x.

$$-149x+429=40$$

Subtract 429 from both sides.

$$-149x=40-429$$

Subtract 429 from 40 to get -389.

$$-149x=-389$$

Divide both sides by -149.

$$x=\frac{-389}{-149}$$

Fraction \frac{-389}{-149} can be simplified to \frac{389}{149} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{389}{149}$$