Solve 2/3(3n-15)=3/4(4n-7)

$$\frac { 2 } { 3 } ( 3 n - 15 ) = \frac { 3 } { 4 } ( 4 n - 7 )$$

Solve for n

$$n = -\frac{19}{4} = -4\frac{3}{4} = -4.75$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 3n-15.

$$\frac{2}{3}\times 3n+\frac{2}{3}\left(-15\right)=\frac{3}{4}\left(4n-7\right)$$

Cancel out 3 and 3.

$$2n+\frac{2}{3}\left(-15\right)=\frac{3}{4}\left(4n-7\right)$$

Express \frac{2}{3}\left(-15\right) as a single fraction.

$$2n+\frac{2\left(-15\right)}{3}=\frac{3}{4}\left(4n-7\right)$$

Multiply 2 and -15 to get -30.

$$2n+\frac{-30}{3}=\frac{3}{4}\left(4n-7\right)$$

Divide -30 by 3 to get -10.

$$2n-10=\frac{3}{4}\left(4n-7\right)$$

Use the distributive property to multiply \frac{3}{4} by 4n-7.

$$2n-10=\frac{3}{4}\times 4n+\frac{3}{4}\left(-7\right)$$

Cancel out 4 and 4.

$$2n-10=3n+\frac{3}{4}\left(-7\right)$$

Express \frac{3}{4}\left(-7\right) as a single fraction.

$$2n-10=3n+\frac{3\left(-7\right)}{4}$$

Multiply 3 and -7 to get -21.

$$2n-10=3n+\frac{-21}{4}$$

Fraction \frac{-21}{4} can be rewritten as -\frac{21}{4} by extracting the negative sign.

$$2n-10=3n-\frac{21}{4}$$

Subtract 3n from both sides.

$$2n-10-3n=-\frac{21}{4}$$

Combine 2n and -3n to get -n.

$$-n-10=-\frac{21}{4}$$

Add 10 to both sides.

$$-n=-\frac{21}{4}+10$$

Convert 10 to fraction \frac{40}{4}.

$$-n=-\frac{21}{4}+\frac{40}{4}$$

Since -\frac{21}{4} and \frac{40}{4} have the same denominator, add them by adding their numerators.

$$-n=\frac{-21+40}{4}$$

Add -21 and 40 to get 19.

$$-n=\frac{19}{4}$$

Multiply both sides by -1.

$$n=-\frac{19}{4}$$