Solve 5x-4/7+7-x/2=5-x+1/6

$$\frac { 5 x - 4 } { 7 } + \frac { 7 - x } { 2 } = 5 - \frac { x + 1 } { 6 }$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 42, the least common multiple of 7,2,6.

$$6\left(5x-4\right)+21\left(7-x\right)=210-7\left(x+1\right)$$

Use the distributive property to multiply 6 by 5x-4.

$$30x-24+21\left(7-x\right)=210-7\left(x+1\right)$$

Use the distributive property to multiply 21 by 7-x.

$$30x-24+147-21x=210-7\left(x+1\right)$$

Add -24 and 147 to get 123.

$$30x+123-21x=210-7\left(x+1\right)$$

Combine 30x and -21x to get 9x.

$$9x+123=210-7\left(x+1\right)$$

Use the distributive property to multiply -7 by x+1.

$$9x+123=210-7x-7$$

Subtract 7 from 210 to get 203.

$$9x+123=203-7x$$

Add 7x to both sides.

$$9x+123+7x=203$$

Combine 9x and 7x to get 16x.

$$16x+123=203$$

Subtract 123 from both sides.

$$16x=203-123$$

Subtract 123 from 203 to get 80.

$$16x=80$$

Divide both sides by 16.

$$x=\frac{80}{16}$$

Divide 80 by 16 to get 5.

$$x=5$$