Solve 12/5(r-2)=2/3[3r-2(2r-1)]

$$\frac { 12 } { 5 } ( r - 2 ) = \frac { 2 } { 3 } [ 3 r - 2 ( 2 r - 1 ) ]$$

Solve for r

$$r=2$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{12}{5} by r-2.

$$\frac{12}{5}r+\frac{12}{5}\left(-2\right)=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Express \frac{12}{5}\left(-2\right) as a single fraction.

$$\frac{12}{5}r+\frac{12\left(-2\right)}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Multiply 12 and -2 to get -24.

$$\frac{12}{5}r+\frac{-24}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Fraction \frac{-24}{5} can be rewritten as -\frac{24}{5} by extracting the negative sign.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(3r-2\left(2r-1\right)\right)$$

Use the distributive property to multiply -2 by 2r-1.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(3r-4r+2\right)$$

Combine 3r and -4r to get -r.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(-r+2\right)$$

Use the distributive property to multiply \frac{2}{3} by -r+2.

$$\frac{12}{5}r-\frac{24}{5}=\frac{2}{3}\left(-1\right)r+\frac{2}{3}\times 2$$

Multiply \frac{2}{3} and -1 to get -\frac{2}{3}.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{2}{3}\times 2$$

Express \frac{2}{3}\times 2 as a single fraction.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{2\times 2}{3}$$

Multiply 2 and 2 to get 4.

$$\frac{12}{5}r-\frac{24}{5}=-\frac{2}{3}r+\frac{4}{3}$$

Add \frac{2}{3}r to both sides.

$$\frac{12}{5}r-\frac{24}{5}+\frac{2}{3}r=\frac{4}{3}$$

Combine \frac{12}{5}r and \frac{2}{3}r to get \frac{46}{15}r.

$$\frac{46}{15}r-\frac{24}{5}=\frac{4}{3}$$

Add \frac{24}{5} to both sides.

$$\frac{46}{15}r=\frac{4}{3}+\frac{24}{5}$$

Least common multiple of 3 and 5 is 15. Convert \frac{4}{3} and \frac{24}{5} to fractions with denominator 15.

$$\frac{46}{15}r=\frac{20}{15}+\frac{72}{15}$$

Since \frac{20}{15} and \frac{72}{15} have the same denominator, add them by adding their numerators.

$$\frac{46}{15}r=\frac{20+72}{15}$$

Add 20 and 72 to get 92.

$$\frac{46}{15}r=\frac{92}{15}$$

Multiply both sides by \frac{15}{46}, the reciprocal of \frac{46}{15}.

$$r=\frac{92}{15}\times \frac{15}{46}$$

Multiply \frac{92}{15} times \frac{15}{46} by multiplying numerator times numerator and denominator times denominator.

$$r=\frac{92\times 15}{15\times 46}$$

Cancel out 15 in both numerator and denominator.

$$r=\frac{92}{46}$$

Divide 92 by 46 to get 2.

$$r=2$$