Solve 2(x-1)/3=40-(3x-4)/5

$$\frac { 2 ( x - 1 ) } { 3 } = 40 - \frac { ( 3 x - 4 ) } { 5 }$$

Solve for x

$$x = \frac{622}{19} = 32\frac{14}{19} \approx 32.736842105$$

Steps for Solving Linear Equation

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

$$5\times 2\left(x-1\right)=600-3\left(3x-4\right)$$

Multiply 5 and 2 to get 10.

$$10\left(x-1\right)=600-3\left(3x-4\right)$$

Use the distributive property to multiply 10 by x-1.

$$10x-10=600-3\left(3x-4\right)$$

Use the distributive property to multiply -3 by 3x-4.

$$10x-10=600-9x+12$$

Add 600 and 12 to get 612.

$$10x-10=612-9x$$

Add 9x to both sides.

$$10x-10+9x=612$$

Combine 10x and 9x to get 19x.

$$19x-10=612$$

Add 10 to both sides.

$$19x=612+10$$

Add 612 and 10 to get 622.

$$19x=622$$

Divide both sides by 19.

$$x=\frac{622}{19}$$