Solve x<1/2(x+6)

$$x < \frac{ 1 }{ 2 } (x+6)$$

Solve for x

$$x<6$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by x+6.

$$x<\frac{1}{2}x+\frac{1}{2}\times 6$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$x<\frac{1}{2}x+\frac{6}{2}$$

Divide 6 by 2 to get 3.

$$x<\frac{1}{2}x+3$$

Subtract \frac{1}{2}x from both sides.

$$x-\frac{1}{2}x<3$$

Combine x and -\frac{1}{2}x to get \frac{1}{2}x.

$$\frac{1}{2}x<3$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}. Since \frac{1}{2} is positive, the inequality direction remains the same.

$$x<3\times 2$$

Multiply 3 and 2 to get 6.

$$x<6$$