Solve 2θ=68/100left(9/5θ+32right)

$$2 \theta = \frac{ 68 }{ 100 } \left( \frac{ 9 }{ 5 } \theta +32 \right)$$

Solve for θ

$$\theta =\frac{2720}{97}\approx 28.041237113$$

Steps for Solving Linear Equation

Reduce the fraction \frac{68}{100} to lowest terms by extracting and canceling out 4.

$$2\theta =\frac{17}{25}\left(\frac{9}{5}\theta +32\right)$$

Use the distributive property to multiply \frac{17}{25} by \frac{9}{5}\theta +32.

$$2\theta =\frac{17}{25}\times \frac{9}{5}\theta +\frac{17}{25}\times 32$$

Multiply \frac{17}{25} times \frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$2\theta =\frac{17\times 9}{25\times 5}\theta +\frac{17}{25}\times 32$$

Do the multiplications in the fraction \frac{17\times 9}{25\times 5}.

$$2\theta =\frac{153}{125}\theta +\frac{17}{25}\times 32$$

Express \frac{17}{25}\times 32 as a single fraction.

$$2\theta =\frac{153}{125}\theta +\frac{17\times 32}{25}$$

Multiply 17 and 32 to get 544.

$$2\theta =\frac{153}{125}\theta +\frac{544}{25}$$

Subtract \frac{153}{125}\theta from both sides.

$$2\theta -\frac{153}{125}\theta =\frac{544}{25}$$

Combine 2\theta and -\frac{153}{125}\theta to get \frac{97}{125}\theta .

$$\frac{97}{125}\theta =\frac{544}{25}$$

Multiply both sides by \frac{125}{97}, the reciprocal of \frac{97}{125}.

$$\theta =\frac{544}{25}\times \frac{125}{97}$$

Multiply \frac{544}{25} times \frac{125}{97} by multiplying numerator times numerator and denominator times denominator.

$$\theta =\frac{544\times 125}{25\times 97}$$

Do the multiplications in the fraction \frac{544\times 125}{25\times 97}.

$$\theta =\frac{68000}{2425}$$

Reduce the fraction \frac{68000}{2425} to lowest terms by extracting and canceling out 25.

$$\theta =\frac{2720}{97}$$