Solve -31/5x+71/10=42/9

$$-3 \frac{ 1 }{ 5 } x+7 \frac{ 1 }{ 10 } = 4 \frac{ 2 }{ 9 }$$

Solve for x

$$x=\frac{259}{288}\approx 0.899305556$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 90, the least common multiple of 5,10,9.

$$90\left(-\frac{3\times 5+1}{5}\right)x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Multiply 3 and 5 to get 15.

$$90\left(-\frac{15+1}{5}\right)x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Add 15 and 1 to get 16.

$$90\left(-\frac{16}{5}\right)x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Express 90\left(-\frac{16}{5}\right) as a single fraction.

$$\frac{90\left(-16\right)}{5}x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Multiply 90 and -16 to get -1440.

$$\frac{-1440}{5}x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Divide -1440 by 5 to get -288.

$$-288x+9\left(7\times 10+1\right)=10\left(4\times 9+2\right)$$

Multiply 7 and 10 to get 70.

$$-288x+9\left(70+1\right)=10\left(4\times 9+2\right)$$

Add 70 and 1 to get 71.

$$-288x+9\times 71=10\left(4\times 9+2\right)$$

Multiply 9 and 71 to get 639.

$$-288x+639=10\left(4\times 9+2\right)$$

Multiply 4 and 9 to get 36.

$$-288x+639=10\left(36+2\right)$$

Add 36 and 2 to get 38.

$$-288x+639=10\times 38$$

Multiply 10 and 38 to get 380.

$$-288x+639=380$$

Subtract 639 from both sides.

$$-288x=380-639$$

Subtract 639 from 380 to get -259.

$$-288x=-259$$

Divide both sides by -288.

$$x=\frac{-259}{-288}$$

Fraction \frac{-259}{-288} can be simplified to \frac{259}{288} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{259}{288}$$