Solve (8224-x)*(1+5.6%)=x

$$(8224-x) \times (1+5.6 \% )=x$$

Solve for x

$$x=4224$$

Steps for Solving Linear Equation

Expand \frac{5.6}{100} by multiplying both numerator and the denominator by 10.

$$\left(8224-x\right)\left(1+\frac{56}{1000}\right)=x$$

Reduce the fraction \frac{56}{1000} to lowest terms by extracting and canceling out 8.

$$\left(8224-x\right)\left(1+\frac{7}{125}\right)=x$$

Convert 1 to fraction \frac{125}{125}.

$$\left(8224-x\right)\left(\frac{125}{125}+\frac{7}{125}\right)=x$$

Since \frac{125}{125} and \frac{7}{125} have the same denominator, add them by adding their numerators.

$$\left(8224-x\right)\times \frac{125+7}{125}=x$$

Add 125 and 7 to get 132.

$$\left(8224-x\right)\times \frac{132}{125}=x$$

Use the distributive property to multiply 8224-x by \frac{132}{125}.

$$8224\times \frac{132}{125}-x\times \frac{132}{125}=x$$

Express 8224\times \frac{132}{125} as a single fraction.

$$\frac{8224\times 132}{125}-x\times \frac{132}{125}=x$$

Multiply 8224 and 132 to get 1085568.

$$\frac{1085568}{125}-x\times \frac{132}{125}=x$$

Multiply -1 and \frac{132}{125} to get -\frac{132}{125}.

$$\frac{1085568}{125}-\frac{132}{125}x=x$$

Subtract x from both sides.

$$\frac{1085568}{125}-\frac{132}{125}x-x=0$$

Combine -\frac{132}{125}x and -x to get -\frac{257}{125}x.

$$\frac{1085568}{125}-\frac{257}{125}x=0$$

Subtract \frac{1085568}{125} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{257}{125}x=-\frac{1085568}{125}$$

Multiply both sides by -\frac{125}{257}, the reciprocal of -\frac{257}{125}.

$$x=-\frac{1085568}{125}\left(-\frac{125}{257}\right)$$

Multiply -\frac{1085568}{125} times -\frac{125}{257} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-1085568\left(-125\right)}{125\times 257}$$

Do the multiplications in the fraction \frac{-1085568\left(-125\right)}{125\times 257}.

$$x=\frac{135696000}{32125}$$

Divide 135696000 by 32125 to get 4224.

$$x=4224$$