Solve (x+80)div90%=(x-70)div75%

$$(x+80) \div 90 \% =(x-70) \div 75 \%$$

Solve for x

$$x=820$$

Steps for Solving Linear Equation

Divide x+80 by \frac{90}{100} by multiplying x+80 by the reciprocal of \frac{90}{100}.

$$\frac{\left(x+80\right)\times 100}{90}=\frac{x-70}{\frac{75}{100}}$$

Divide \left(x+80\right)\times 100 by 90 to get \left(x+80\right)\times \frac{10}{9}.

$$\left(x+80\right)\times \frac{10}{9}=\frac{x-70}{\frac{75}{100}}$$

Use the distributive property to multiply x+80 by \frac{10}{9}.

$$x\times \frac{10}{9}+80\times \frac{10}{9}=\frac{x-70}{\frac{75}{100}}$$

Express 80\times \frac{10}{9} as a single fraction.

$$x\times \frac{10}{9}+\frac{80\times 10}{9}=\frac{x-70}{\frac{75}{100}}$$

Multiply 80 and 10 to get 800.

$$x\times \frac{10}{9}+\frac{800}{9}=\frac{x-70}{\frac{75}{100}}$$

Divide x-70 by \frac{75}{100} by multiplying x-70 by the reciprocal of \frac{75}{100}.

$$x\times \frac{10}{9}+\frac{800}{9}=\frac{\left(x-70\right)\times 100}{75}$$

Divide \left(x-70\right)\times 100 by 75 to get \left(x-70\right)\times \frac{4}{3}.

$$x\times \frac{10}{9}+\frac{800}{9}=\left(x-70\right)\times \frac{4}{3}$$

Use the distributive property to multiply x-70 by \frac{4}{3}.

$$x\times \frac{10}{9}+\frac{800}{9}=x\times \frac{4}{3}-70\times \frac{4}{3}$$

Express -70\times \frac{4}{3} as a single fraction.

$$x\times \frac{10}{9}+\frac{800}{9}=x\times \frac{4}{3}+\frac{-70\times 4}{3}$$

Multiply -70 and 4 to get -280.

$$x\times \frac{10}{9}+\frac{800}{9}=x\times \frac{4}{3}+\frac{-280}{3}$$

Fraction \frac{-280}{3} can be rewritten as -\frac{280}{3} by extracting the negative sign.

$$x\times \frac{10}{9}+\frac{800}{9}=x\times \frac{4}{3}-\frac{280}{3}$$

Subtract x\times \frac{4}{3} from both sides.

$$x\times \frac{10}{9}+\frac{800}{9}-x\times \frac{4}{3}=-\frac{280}{3}$$

Combine x\times \frac{10}{9} and -x\times \frac{4}{3} to get -\frac{2}{9}x.

$$-\frac{2}{9}x+\frac{800}{9}=-\frac{280}{3}$$

Subtract \frac{800}{9} from both sides.

$$-\frac{2}{9}x=-\frac{280}{3}-\frac{800}{9}$$

Least common multiple of 3 and 9 is 9. Convert -\frac{280}{3} and \frac{800}{9} to fractions with denominator 9.

$$-\frac{2}{9}x=-\frac{840}{9}-\frac{800}{9}$$

Since -\frac{840}{9} and \frac{800}{9} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{2}{9}x=\frac{-840-800}{9}$$

Subtract 800 from -840 to get -1640.

$$-\frac{2}{9}x=-\frac{1640}{9}$$

Multiply both sides by -\frac{9}{2}, the reciprocal of -\frac{2}{9}.

$$x=-\frac{1640}{9}\left(-\frac{9}{2}\right)$$

Multiply -\frac{1640}{9} times -\frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-1640\left(-9\right)}{9\times 2}$$

Do the multiplications in the fraction \frac{-1640\left(-9\right)}{9\times 2}.

$$x=\frac{14760}{18}$$

Divide 14760 by 18 to get 820.

$$x=820$$