Solve 2/5(2x-5)-1/4(x+2)=2/3(x-1)

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

Solve for x

$$x = -\frac{110}{7} = -15\frac{5}{7} \approx -15.714285714$$

Steps for Solving Linear Equation

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

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

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

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

Multiply 2 and 2 to get 4.

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

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

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

Multiply 2 and -5 to get -10.

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

Divide -10 by 5 to get -2.

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

Use the distributive property to multiply -\frac{1}{4} by x+2.

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

Express -\frac{1}{4}\times 2 as a single fraction.

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

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

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

Combine \frac{4}{5}x and -\frac{1}{4}x to get \frac{11}{20}x.

$$\frac{11}{20}x-2-\frac{1}{2}=\frac{2}{3}\left(x-1\right)$$

Convert -2 to fraction -\frac{4}{2}.

$$\frac{11}{20}x-\frac{4}{2}-\frac{1}{2}=\frac{2}{3}\left(x-1\right)$$

Since -\frac{4}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11}{20}x+\frac{-4-1}{2}=\frac{2}{3}\left(x-1\right)$$

Subtract 1 from -4 to get -5.

$$\frac{11}{20}x-\frac{5}{2}=\frac{2}{3}\left(x-1\right)$$

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

$$\frac{11}{20}x-\frac{5}{2}=\frac{2}{3}x+\frac{2}{3}\left(-1\right)$$

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

$$\frac{11}{20}x-\frac{5}{2}=\frac{2}{3}x-\frac{2}{3}$$

Subtract \frac{2}{3}x from both sides.

$$\frac{11}{20}x-\frac{5}{2}-\frac{2}{3}x=-\frac{2}{3}$$

Combine \frac{11}{20}x and -\frac{2}{3}x to get -\frac{7}{60}x.

$$-\frac{7}{60}x-\frac{5}{2}=-\frac{2}{3}$$

Add \frac{5}{2} to both sides.

$$-\frac{7}{60}x=-\frac{2}{3}+\frac{5}{2}$$

Least common multiple of 3 and 2 is 6. Convert -\frac{2}{3} and \frac{5}{2} to fractions with denominator 6.

$$-\frac{7}{60}x=-\frac{4}{6}+\frac{15}{6}$$

Since -\frac{4}{6} and \frac{15}{6} have the same denominator, add them by adding their numerators.

$$-\frac{7}{60}x=\frac{-4+15}{6}$$

Add -4 and 15 to get 11.

$$-\frac{7}{60}x=\frac{11}{6}$$

Multiply both sides by -\frac{60}{7}, the reciprocal of -\frac{7}{60}.

$$x=\frac{11}{6}\left(-\frac{60}{7}\right)$$

Multiply \frac{11}{6} times -\frac{60}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{11\left(-60\right)}{6\times 7}$$

Do the multiplications in the fraction \frac{11\left(-60\right)}{6\times 7}.

$$x=\frac{-660}{42}$$

Reduce the fraction \frac{-660}{42} to lowest terms by extracting and canceling out 6.

$$x=-\frac{110}{7}$$