Solve 3x-11/20-5x+1/14=x-7/10-5x-6/21

$$\frac{ 3x-11 }{ 20 } - \frac{ 5x+1 }{ 14 } = \frac{ x-7 }{ 10 } - \frac{ 5x-6 }{ 21 }$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 420, the least common multiple of 20,14,10,21.

$$21\left(3x-11\right)-30\left(5x+1\right)=42\left(x-7\right)-20\left(5x-6\right)$$

Use the distributive property to multiply 21 by 3x-11.

$$63x-231-30\left(5x+1\right)=42\left(x-7\right)-20\left(5x-6\right)$$

Use the distributive property to multiply -30 by 5x+1.

$$63x-231-150x-30=42\left(x-7\right)-20\left(5x-6\right)$$

Combine 63x and -150x to get -87x.

$$-87x-231-30=42\left(x-7\right)-20\left(5x-6\right)$$

Subtract 30 from -231 to get -261.

$$-87x-261=42\left(x-7\right)-20\left(5x-6\right)$$

Use the distributive property to multiply 42 by x-7.

$$-87x-261=42x-294-20\left(5x-6\right)$$

Use the distributive property to multiply -20 by 5x-6.

$$-87x-261=42x-294-100x+120$$

Combine 42x and -100x to get -58x.

$$-87x-261=-58x-294+120$$

Add -294 and 120 to get -174.

$$-87x-261=-58x-174$$

Add 58x to both sides.

$$-87x-261+58x=-174$$

Combine -87x and 58x to get -29x.

$$-29x-261=-174$$

Add 261 to both sides.

$$-29x=-174+261$$

Add -174 and 261 to get 87.

$$-29x=87$$

Divide both sides by -29.

$$x=\frac{87}{-29}$$

Divide 87 by -29 to get -3.

$$x=-3$$