Solve 1/4x+1/3(64-x)=x-46

$$\frac { 1 } { 4 } x + \frac { 1 } { 3 } ( 64 - x ) = x - 46$$

Solve for x

$$x = \frac{808}{13} = 62\frac{2}{13} \approx 62.153846154$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{3} by 64-x.

$$\frac{1}{4}x+\frac{1}{3}\times 64+\frac{1}{3}\left(-1\right)x=x-46$$

Multiply \frac{1}{3} and 64 to get \frac{64}{3}.

$$\frac{1}{4}x+\frac{64}{3}+\frac{1}{3}\left(-1\right)x=x-46$$

Multiply \frac{1}{3} and -1 to get -\frac{1}{3}.

$$\frac{1}{4}x+\frac{64}{3}-\frac{1}{3}x=x-46$$

Combine \frac{1}{4}x and -\frac{1}{3}x to get -\frac{1}{12}x.

$$-\frac{1}{12}x+\frac{64}{3}=x-46$$

Subtract x from both sides.

$$-\frac{1}{12}x+\frac{64}{3}-x=-46$$

Combine -\frac{1}{12}x and -x to get -\frac{13}{12}x.

$$-\frac{13}{12}x+\frac{64}{3}=-46$$

Subtract \frac{64}{3} from both sides.

$$-\frac{13}{12}x=-46-\frac{64}{3}$$

Convert -46 to fraction -\frac{138}{3}.

$$-\frac{13}{12}x=-\frac{138}{3}-\frac{64}{3}$$

Since -\frac{138}{3} and \frac{64}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{12}x=\frac{-138-64}{3}$$

Subtract 64 from -138 to get -202.

$$-\frac{13}{12}x=-\frac{202}{3}$$

Multiply both sides by -\frac{12}{13}, the reciprocal of -\frac{13}{12}.

$$x=-\frac{202}{3}\left(-\frac{12}{13}\right)$$

Multiply -\frac{202}{3} times -\frac{12}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-202\left(-12\right)}{3\times 13}$$

Do the multiplications in the fraction \frac{-202\left(-12\right)}{3\times 13}.

$$x=\frac{2424}{39}$$

Reduce the fraction \frac{2424}{39} to lowest terms by extracting and canceling out 3.

$$x=\frac{808}{13}$$