Solve 2-3x-7/4=x+17/5

$$2- \frac{ 3x-7 }{ 4 } = \frac{ x+17 }{ 5 }$$

Solve for x

$$x=\frac{7}{19}\approx 0.368421053$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 4,5.

$$40-5\left(3x-7\right)=4\left(x+17\right)$$

Use the distributive property to multiply -5 by 3x-7.

$$40-15x+35=4\left(x+17\right)$$

Add 40 and 35 to get 75.

$$75-15x=4\left(x+17\right)$$

Use the distributive property to multiply 4 by x+17.

$$75-15x=4x+68$$

Subtract 4x from both sides.

$$75-15x-4x=68$$

Combine -15x and -4x to get -19x.

$$75-19x=68$$

Subtract 75 from both sides.

$$-19x=68-75$$

Subtract 75 from 68 to get -7.

$$-19x=-7$$

Divide both sides by -19.

$$x=\frac{-7}{-19}$$

Fraction \frac{-7}{-19} can be simplified to \frac{7}{19} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{7}{19}$$