Solve (8224-x)*(1+56%)=x

$$(8224-x) \times (1+56 \% )=x$$

Solve for x

$$x = \frac{10023}{2} = 5011\frac{1}{2} = 5011.5$$

Steps for Solving Linear Equation

Reduce the fraction \frac{56}{100} to lowest terms by extracting and canceling out 4.

$$\left(8224-x\right)\left(1+\frac{14}{25}\right)=x$$

Convert 1 to fraction \frac{25}{25}.

$$\left(8224-x\right)\left(\frac{25}{25}+\frac{14}{25}\right)=x$$

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

$$\left(8224-x\right)\times \frac{25+14}{25}=x$$

Add 25 and 14 to get 39.

$$\left(8224-x\right)\times \frac{39}{25}=x$$

Use the distributive property to multiply 8224-x by \frac{39}{25}.

$$8224\times \frac{39}{25}-x\times \frac{39}{25}=x$$

Express 8224\times \frac{39}{25} as a single fraction.

$$\frac{8224\times 39}{25}-x\times \frac{39}{25}=x$$

Multiply 8224 and 39 to get 320736.

$$\frac{320736}{25}-x\times \frac{39}{25}=x$$

Multiply -1 and \frac{39}{25} to get -\frac{39}{25}.

$$\frac{320736}{25}-\frac{39}{25}x=x$$

Subtract x from both sides.

$$\frac{320736}{25}-\frac{39}{25}x-x=0$$

Combine -\frac{39}{25}x and -x to get -\frac{64}{25}x.

$$\frac{320736}{25}-\frac{64}{25}x=0$$

Subtract \frac{320736}{25} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{64}{25}x=-\frac{320736}{25}$$

Multiply both sides by -\frac{25}{64}, the reciprocal of -\frac{64}{25}.

$$x=-\frac{320736}{25}\left(-\frac{25}{64}\right)$$

Multiply -\frac{320736}{25} times -\frac{25}{64} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-320736\left(-25\right)}{25\times 64}$$

Do the multiplications in the fraction \frac{-320736\left(-25\right)}{25\times 64}.

$$x=\frac{8018400}{1600}$$

Reduce the fraction \frac{8018400}{1600} to lowest terms by extracting and canceling out 800.

$$x=\frac{10023}{2}$$