Solve x+3/4=1+3x+6/5

$$\frac { x + 3 } { 4 } = 1 + \frac { 3 x + 6 } { 5 }$$

Solve for x

$$x = -\frac{29}{7} = -4\frac{1}{7} \approx -4.142857143$$

Steps for Solving Linear Equation

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

$$5\left(x+3\right)=20+4\left(3x+6\right)$$

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

$$5x+15=20+4\left(3x+6\right)$$

Use the distributive property to multiply 4 by 3x+6.

$$5x+15=20+12x+24$$

Add 20 and 24 to get 44.

$$5x+15=44+12x$$

Subtract 12x from both sides.

$$5x+15-12x=44$$

Combine 5x and -12x to get -7x.

$$-7x+15=44$$

Subtract 15 from both sides.

$$-7x=44-15$$

Subtract 15 from 44 to get 29.

$$-7x=29$$

Divide both sides by -7.

$$x=\frac{29}{-7}$$

Fraction \frac{29}{-7} can be rewritten as -\frac{29}{7} by extracting the negative sign.

$$x=-\frac{29}{7}$$