Solve a*235=[a*235+(1-a)238]*2*34%

$$a \cdot 235 = [ a \cdot 235 + ( 1 - a ) 238 ] \times 2 \cdot 34 \%$$

Solve for a

$$a=\frac{2023}{2963}\approx 0.682753966$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1-a by 238.

$$a\times 235=\left(a\times 235+238-238a\right)\times 2\times \frac{34}{100}$$

Combine a\times 235 and -238a to get -3a.

$$a\times 235=\left(-3a+238\right)\times 2\times \frac{34}{100}$$

Reduce the fraction \frac{34}{100} to lowest terms by extracting and canceling out 2.

$$a\times 235=\left(-3a+238\right)\times 2\times \frac{17}{50}$$

Express 2\times \frac{17}{50} as a single fraction.

$$a\times 235=\left(-3a+238\right)\times \frac{2\times 17}{50}$$

Multiply 2 and 17 to get 34.

$$a\times 235=\left(-3a+238\right)\times \frac{34}{50}$$

Reduce the fraction \frac{34}{50} to lowest terms by extracting and canceling out 2.

$$a\times 235=\left(-3a+238\right)\times \frac{17}{25}$$

Use the distributive property to multiply -3a+238 by \frac{17}{25}.

$$a\times 235=-3a\times \frac{17}{25}+238\times \frac{17}{25}$$

Express -3\times \frac{17}{25} as a single fraction.

$$a\times 235=\frac{-3\times 17}{25}a+238\times \frac{17}{25}$$

Multiply -3 and 17 to get -51.

$$a\times 235=\frac{-51}{25}a+238\times \frac{17}{25}$$

Fraction \frac{-51}{25} can be rewritten as -\frac{51}{25} by extracting the negative sign.

$$a\times 235=-\frac{51}{25}a+238\times \frac{17}{25}$$

Express 238\times \frac{17}{25} as a single fraction.

$$a\times 235=-\frac{51}{25}a+\frac{238\times 17}{25}$$

Multiply 238 and 17 to get 4046.

$$a\times 235=-\frac{51}{25}a+\frac{4046}{25}$$

Add \frac{51}{25}a to both sides.

$$a\times 235+\frac{51}{25}a=\frac{4046}{25}$$

Combine a\times 235 and \frac{51}{25}a to get \frac{5926}{25}a.

$$\frac{5926}{25}a=\frac{4046}{25}$$

Multiply both sides by \frac{25}{5926}, the reciprocal of \frac{5926}{25}.

$$a=\frac{4046}{25}\times \frac{25}{5926}$$

Multiply \frac{4046}{25} times \frac{25}{5926} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{4046\times 25}{25\times 5926}$$

Cancel out 25 in both numerator and denominator.

$$a=\frac{4046}{5926}$$

Reduce the fraction \frac{4046}{5926} to lowest terms by extracting and canceling out 2.

$$a=\frac{2023}{2963}$$