Solve 50%*(165-x)+1/4x=50

$$50 \% \cdot ( 165 - x ) + \frac { 1 } { 4 } x = 50$$

Solve for x

$$x=130$$

Steps for Solving Linear Equation

Reduce the fraction \frac{50}{100} to lowest terms by extracting and canceling out 50.

$$\frac{1}{2}\left(165-x\right)+\frac{1}{4}x=50$$

Use the distributive property to multiply \frac{1}{2} by 165-x.

$$\frac{1}{2}\times 165+\frac{1}{2}\left(-1\right)x+\frac{1}{4}x=50$$

Multiply \frac{1}{2} and 165 to get \frac{165}{2}.

$$\frac{165}{2}+\frac{1}{2}\left(-1\right)x+\frac{1}{4}x=50$$

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

$$\frac{165}{2}-\frac{1}{2}x+\frac{1}{4}x=50$$

Combine -\frac{1}{2}x and \frac{1}{4}x to get -\frac{1}{4}x.

$$\frac{165}{2}-\frac{1}{4}x=50$$

Subtract \frac{165}{2} from both sides.

$$-\frac{1}{4}x=50-\frac{165}{2}$$

Convert 50 to fraction \frac{100}{2}.

$$-\frac{1}{4}x=\frac{100}{2}-\frac{165}{2}$$

Since \frac{100}{2} and \frac{165}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{4}x=\frac{100-165}{2}$$

Subtract 165 from 100 to get -65.

$$-\frac{1}{4}x=-\frac{65}{2}$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}.

$$x=-\frac{65}{2}\left(-4\right)$$

Express -\frac{65}{2}\left(-4\right) as a single fraction.

$$x=\frac{-65\left(-4\right)}{2}$$

Multiply -65 and -4 to get 260.

$$x=\frac{260}{2}$$

Divide 260 by 2 to get 130.

$$x=130$$