Solve 2/3left(5x-1right)-4/5left(2x-3right)=0=

$$\frac{ 2 }{ 3 } \left( 5x-1 \right) - \frac{ 4 }{ 5 } \left( 2x-3 \right) =0=$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 5x-1.

$$\frac{2}{3}\times 5x+\frac{2}{3}\left(-1\right)-\frac{4}{5}\left(2x-3\right)=0$$

Express \frac{2}{3}\times 5 as a single fraction.

$$\frac{2\times 5}{3}x+\frac{2}{3}\left(-1\right)-\frac{4}{5}\left(2x-3\right)=0$$

Multiply 2 and 5 to get 10.

$$\frac{10}{3}x+\frac{2}{3}\left(-1\right)-\frac{4}{5}\left(2x-3\right)=0$$

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

$$\frac{10}{3}x-\frac{2}{3}-\frac{4}{5}\left(2x-3\right)=0$$

Use the distributive property to multiply -\frac{4}{5} by 2x-3.

$$\frac{10}{3}x-\frac{2}{3}-\frac{4}{5}\times 2x-\frac{4}{5}\left(-3\right)=0$$

Express -\frac{4}{5}\times 2 as a single fraction.

$$\frac{10}{3}x-\frac{2}{3}+\frac{-4\times 2}{5}x-\frac{4}{5}\left(-3\right)=0$$

Multiply -4 and 2 to get -8.

$$\frac{10}{3}x-\frac{2}{3}+\frac{-8}{5}x-\frac{4}{5}\left(-3\right)=0$$

Fraction \frac{-8}{5} can be rewritten as -\frac{8}{5} by extracting the negative sign.

$$\frac{10}{3}x-\frac{2}{3}-\frac{8}{5}x-\frac{4}{5}\left(-3\right)=0$$

Express -\frac{4}{5}\left(-3\right) as a single fraction.

$$\frac{10}{3}x-\frac{2}{3}-\frac{8}{5}x+\frac{-4\left(-3\right)}{5}=0$$

Multiply -4 and -3 to get 12.

$$\frac{10}{3}x-\frac{2}{3}-\frac{8}{5}x+\frac{12}{5}=0$$

Combine \frac{10}{3}x and -\frac{8}{5}x to get \frac{26}{15}x.

$$\frac{26}{15}x-\frac{2}{3}+\frac{12}{5}=0$$

Least common multiple of 3 and 5 is 15. Convert -\frac{2}{3} and \frac{12}{5} to fractions with denominator 15.

$$\frac{26}{15}x-\frac{10}{15}+\frac{36}{15}=0$$

Since -\frac{10}{15} and \frac{36}{15} have the same denominator, add them by adding their numerators.

$$\frac{26}{15}x+\frac{-10+36}{15}=0$$

Add -10 and 36 to get 26.

$$\frac{26}{15}x+\frac{26}{15}=0$$

Subtract \frac{26}{15} from both sides. Anything subtracted from zero gives its negation.

$$\frac{26}{15}x=-\frac{26}{15}$$

Multiply both sides by \frac{15}{26}, the reciprocal of \frac{26}{15}.

$$x=-\frac{26}{15}\times \frac{15}{26}$$

Multiply -\frac{26}{15} times \frac{15}{26} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-26\times 15}{15\times 26}$$

Cancel out 15 in both numerator and denominator.

$$x=\frac{-26}{26}$$

Divide -26 by 26 to get -1.

$$x=-1$$