Solve x-7=1/2left(x-7right)+16

$$x-7 = \frac{ 1 }{ 2 } \left( x-7 \right) +16$$

Solve for x

$$x=39$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{2} by x-7.

$$x-7=\frac{1}{2}x+\frac{1}{2}\left(-7\right)+16$$

Multiply \frac{1}{2} and -7 to get \frac{-7}{2}.

$$x-7=\frac{1}{2}x+\frac{-7}{2}+16$$

Fraction \frac{-7}{2} can be rewritten as -\frac{7}{2} by extracting the negative sign.

$$x-7=\frac{1}{2}x-\frac{7}{2}+16$$

Convert 16 to fraction \frac{32}{2}.

$$x-7=\frac{1}{2}x-\frac{7}{2}+\frac{32}{2}$$

Since -\frac{7}{2} and \frac{32}{2} have the same denominator, add them by adding their numerators.

$$x-7=\frac{1}{2}x+\frac{-7+32}{2}$$

Add -7 and 32 to get 25.

$$x-7=\frac{1}{2}x+\frac{25}{2}$$

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

$$x-7-\frac{1}{2}x=\frac{25}{2}$$

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

$$\frac{1}{2}x-7=\frac{25}{2}$$

Add 7 to both sides.

$$\frac{1}{2}x=\frac{25}{2}+7$$

Convert 7 to fraction \frac{14}{2}.

$$\frac{1}{2}x=\frac{25}{2}+\frac{14}{2}$$

Since \frac{25}{2} and \frac{14}{2} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x=\frac{25+14}{2}$$

Add 25 and 14 to get 39.

$$\frac{1}{2}x=\frac{39}{2}$$

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

$$x=\frac{39}{2}\times 2$$

Cancel out 2 and 2.

$$x=39$$