Solve 1.4x*80%+(210-1.4x)*90%=182

$$1.4x \times 80 \% +(210-1.4x) \times 90 \% =182$$

Solve for x

$$x=50$$

Steps for Solving Linear Equation

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$1.4x\times \frac{4}{5}+\left(210-1.4x\right)\times \frac{90}{100}=182$$

Convert decimal number 1.4 to fraction \frac{14}{10}. Reduce the fraction \frac{14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{7}{5}x\times \frac{4}{5}+\left(210-1.4x\right)\times \frac{90}{100}=182$$

Multiply \frac{7}{5} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\times 4}{5\times 5}x+\left(210-1.4x\right)\times \frac{90}{100}=182$$

Do the multiplications in the fraction \frac{7\times 4}{5\times 5}.

$$\frac{28}{25}x+\left(210-1.4x\right)\times \frac{90}{100}=182$$

Reduce the fraction \frac{90}{100} to lowest terms by extracting and canceling out 10.

$$\frac{28}{25}x+\left(210-1.4x\right)\times \frac{9}{10}=182$$

Use the distributive property to multiply 210-1.4x by \frac{9}{10}.

$$\frac{28}{25}x+210\times \frac{9}{10}-1.4x\times \frac{9}{10}=182$$

Express 210\times \frac{9}{10} as a single fraction.

$$\frac{28}{25}x+\frac{210\times 9}{10}-1.4x\times \frac{9}{10}=182$$

Multiply 210 and 9 to get 1890.

$$\frac{28}{25}x+\frac{1890}{10}-1.4x\times \frac{9}{10}=182$$

Divide 1890 by 10 to get 189.

$$\frac{28}{25}x+189-1.4x\times \frac{9}{10}=182$$

Convert decimal number -1.4 to fraction -\frac{14}{10}. Reduce the fraction -\frac{14}{10} to lowest terms by extracting and canceling out 2.

$$\frac{28}{25}x+189-\frac{7}{5}x\times \frac{9}{10}=182$$

Multiply -\frac{7}{5} times \frac{9}{10} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28}{25}x+189+\frac{-7\times 9}{5\times 10}x=182$$

Do the multiplications in the fraction \frac{-7\times 9}{5\times 10}.

$$\frac{28}{25}x+189+\frac{-63}{50}x=182$$

Fraction \frac{-63}{50} can be rewritten as -\frac{63}{50} by extracting the negative sign.

$$\frac{28}{25}x+189-\frac{63}{50}x=182$$

Combine \frac{28}{25}x and -\frac{63}{50}x to get -\frac{7}{50}x.

$$-\frac{7}{50}x+189=182$$

Subtract 189 from both sides.

$$-\frac{7}{50}x=182-189$$

Subtract 189 from 182 to get -7.

$$-\frac{7}{50}x=-7$$

Multiply both sides by -\frac{50}{7}, the reciprocal of -\frac{7}{50}.

$$x=-7\left(-\frac{50}{7}\right)$$

Multiply -7 times -\frac{50}{7}.

$$x=50$$