Solve 16quad1/2(x-1)-(x-3)=1/3(x+3)+1/6

$$16 \quad \frac { 1 } { 2 } ( x - 1 ) - ( x - 3 ) = \frac { 1 } { 3 } ( x + 3 ) + \frac { 1 } { 6 }$$

Solve for x

$$x=\frac{88}{91}\approx 0.967032967$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3,6.

$$3\left(16\times 2+1\right)\left(x-1\right)-6\left(x-3\right)=2\left(x+3\right)+1$$

Multiply 16 and 2 to get 32.

$$3\left(32+1\right)\left(x-1\right)-6\left(x-3\right)=2\left(x+3\right)+1$$

Add 32 and 1 to get 33.

$$3\times 33\left(x-1\right)-6\left(x-3\right)=2\left(x+3\right)+1$$

Multiply 3 and 33 to get 99.

$$99\left(x-1\right)-6\left(x-3\right)=2\left(x+3\right)+1$$

Use the distributive property to multiply 99 by x-1.

$$99x-99-6\left(x-3\right)=2\left(x+3\right)+1$$

Use the distributive property to multiply -6 by x-3.

$$99x-99-6x+18=2\left(x+3\right)+1$$

Combine 99x and -6x to get 93x.

$$93x-99+18=2\left(x+3\right)+1$$

Add -99 and 18 to get -81.

$$93x-81=2\left(x+3\right)+1$$

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

$$93x-81=2x+6+1$$

Add 6 and 1 to get 7.

$$93x-81=2x+7$$

Subtract 2x from both sides.

$$93x-81-2x=7$$

Combine 93x and -2x to get 91x.

$$91x-81=7$$

Add 81 to both sides.

$$91x=7+81$$

Add 7 and 81 to get 88.

$$91x=88$$

Divide both sides by 91.

$$x=\frac{88}{91}$$