Solve 5.3left(10.9r-2right)=11.5

$$5.3 \left( 10.9r-2 \right) = 11.5$$

Solve for r

$$r=\frac{2210}{5777}\approx 0.382551497$$

Steps for Solving Linear Equation

Divide both sides by 5.3.

$$10.9r-2=\frac{11.5}{5.3}$$

Expand \frac{11.5}{5.3} by multiplying both numerator and the denominator by 10.

$$10.9r-2=\frac{115}{53}$$

Add 2 to both sides.

$$10.9r=\frac{115}{53}+2$$

Convert 2 to fraction \frac{106}{53}.

$$10.9r=\frac{115}{53}+\frac{106}{53}$$

Since \frac{115}{53} and \frac{106}{53} have the same denominator, add them by adding their numerators.

$$10.9r=\frac{115+106}{53}$$

Add 115 and 106 to get 221.

$$10.9r=\frac{221}{53}$$

Divide both sides by 10.9.

$$r=\frac{\frac{221}{53}}{10.9}$$

Express \frac{\frac{221}{53}}{10.9} as a single fraction.

$$r=\frac{221}{53\times 10.9}$$

Multiply 53 and 10.9 to get 577.7.

$$r=\frac{221}{577.7}$$

Expand \frac{221}{577.7} by multiplying both numerator and the denominator by 10.

$$r=\frac{2210}{5777}$$