Solve 5(x-4)-3(2x+4)/1+2x=3/7

$$\frac { 5 ( x - 4 ) - 3 ( 2 x + 4 ) } { 1 + 2 x } = \frac { 3 } { 7 }$$

Solve for x

$$x = -\frac{227}{13} = -17\frac{6}{13} \approx -17.461538462$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 7\left(2x+1\right), the least common multiple of 1+2x,7.

$$7\left(5\left(x-4\right)-3\left(2x+4\right)\right)=3\left(2x+1\right)$$

Use the distributive property to multiply 5 by x-4.

$$7\left(5x-20-3\left(2x+4\right)\right)=3\left(2x+1\right)$$

Use the distributive property to multiply -3 by 2x+4.

$$7\left(5x-20-6x-12\right)=3\left(2x+1\right)$$

Combine 5x and -6x to get -x.

$$7\left(-x-20-12\right)=3\left(2x+1\right)$$

Subtract 12 from -20 to get -32.

$$7\left(-x-32\right)=3\left(2x+1\right)$$

Use the distributive property to multiply 7 by -x-32.

$$-7x-224=3\left(2x+1\right)$$

Use the distributive property to multiply 3 by 2x+1.

$$-7x-224=6x+3$$

Subtract 6x from both sides.

$$-7x-224-6x=3$$

Combine -7x and -6x to get -13x.

$$-13x-224=3$$

Add 224 to both sides.

$$-13x=3+224$$

Add 3 and 224 to get 227.

$$-13x=227$$

Divide both sides by -13.

$$x=\frac{227}{-13}$$

Fraction \frac{227}{-13} can be rewritten as -\frac{227}{13} by extracting the negative sign.

$$x=-\frac{227}{13}$$