Solve 9+x=1/2*(35+x)7

$$9 + x = \frac { 1 } { 2 } \cdot ( 35 + x ) 7$$

Solve for x

$$x = -\frac{227}{5} = -45\frac{2}{5} = -45.4$$

Steps for Solving Linear Equation

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

$$9+x=\frac{7}{2}\left(35+x\right)$$

Use the distributive property to multiply \frac{7}{2} by 35+x.

$$9+x=\frac{7}{2}\times 35+\frac{7}{2}x$$

Express \frac{7}{2}\times 35 as a single fraction.

$$9+x=\frac{7\times 35}{2}+\frac{7}{2}x$$

Multiply 7 and 35 to get 245.

$$9+x=\frac{245}{2}+\frac{7}{2}x$$

Subtract \frac{7}{2}x from both sides.

$$9+x-\frac{7}{2}x=\frac{245}{2}$$

Combine x and -\frac{7}{2}x to get -\frac{5}{2}x.

$$9-\frac{5}{2}x=\frac{245}{2}$$

Subtract 9 from both sides.

$$-\frac{5}{2}x=\frac{245}{2}-9$$

Convert 9 to fraction \frac{18}{2}.

$$-\frac{5}{2}x=\frac{245}{2}-\frac{18}{2}$$

Since \frac{245}{2} and \frac{18}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{2}x=\frac{245-18}{2}$$

Subtract 18 from 245 to get 227.

$$-\frac{5}{2}x=\frac{227}{2}$$

Multiply both sides by -\frac{2}{5}, the reciprocal of -\frac{5}{2}.

$$x=\frac{227}{2}\left(-\frac{2}{5}\right)$$

Multiply \frac{227}{2} times -\frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{227\left(-2\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{227\left(-2\right)}{2\times 5}.

$$x=\frac{-454}{10}$$

Reduce the fraction \frac{-454}{10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{227}{5}$$