Solve 1/2left(x+1right)-4/3div1/6=2

$$\frac{ 1 }{ 2 } \left( x+1 \right) - \frac{ 4 }{ 3 } \div \frac{ 1 }{ 6 } = 2$$

Solve for x

$$x=19$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x+1.

$$\frac{1}{2}x+\frac{1}{2}-\frac{\frac{4}{3}}{\frac{1}{6}}=2$$

Divide \frac{4}{3} by \frac{1}{6} by multiplying \frac{4}{3} by the reciprocal of \frac{1}{6}.

$$\frac{1}{2}x+\frac{1}{2}-\frac{4}{3}\times 6=2$$

Express \frac{4}{3}\times 6 as a single fraction.

$$\frac{1}{2}x+\frac{1}{2}-\frac{4\times 6}{3}=2$$

Multiply 4 and 6 to get 24.

$$\frac{1}{2}x+\frac{1}{2}-\frac{24}{3}=2$$

Divide 24 by 3 to get 8.

$$\frac{1}{2}x+\frac{1}{2}-8=2$$

Convert 8 to fraction \frac{16}{2}.

$$\frac{1}{2}x+\frac{1}{2}-\frac{16}{2}=2$$

Since \frac{1}{2} and \frac{16}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x+\frac{1-16}{2}=2$$

Subtract 16 from 1 to get -15.

$$\frac{1}{2}x-\frac{15}{2}=2$$

Add \frac{15}{2} to both sides.

$$\frac{1}{2}x=2+\frac{15}{2}$$

Convert 2 to fraction \frac{4}{2}.

$$\frac{1}{2}x=\frac{4}{2}+\frac{15}{2}$$

Since \frac{4}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x=\frac{4+15}{2}$$

Add 4 and 15 to get 19.

$$\frac{1}{2}x=\frac{19}{2}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=\frac{19}{2}\times 2$$

Cancel out 2 and 2.

$$x=19$$