Solve r=1.5(10r/6)/2.5

$$r = \frac { 1.5 ( \frac { 10 r } { 6 } ) } { 2.5 }$$

Solve for r

$$r\in \mathrm{R}$$

Solution Steps

Divide 10r by 6 to get \frac{5}{3}r.

$$r=\frac{1.5\times \frac{5}{3}r}{2.5}$$

Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.

$$r=\frac{\frac{3}{2}\times \frac{5}{3}r}{2.5}$$

Multiply \frac{3}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$r=\frac{\frac{3\times 5}{2\times 3}r}{2.5}$$

Cancel out 3 in both numerator and denominator.

$$r=\frac{\frac{5}{2}r}{2.5}$$

Cancel out 2.5 and 2.5.

$$r=r$$

Subtract r from both sides.

$$r-r=0$$

Combine r and -r to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any r.

$$r\in \mathrm{R}$$