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

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

Solve for x

$$x=-\frac{2}{5}=-0.4$$

Steps for Solving Linear Equation

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

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

Express \frac{2}{3}\left(-5\right) as a single fraction.

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

Multiply 2 and -5 to get -10.

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

Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.

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

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

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

Express -\frac{1}{4}\left(-2\right) as a single fraction.

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

Multiply -1 and -2 to get 2.

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{2}{4}=-3$$

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

$$\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{1}{2}=-3$$

Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.

$$\frac{5}{12}x-\frac{10}{3}+\frac{1}{2}=-3$$

Least common multiple of 3 and 2 is 6. Convert -\frac{10}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{5}{12}x-\frac{20}{6}+\frac{3}{6}=-3$$

Since -\frac{20}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x+\frac{-20+3}{6}=-3$$

Add -20 and 3 to get -17.

$$\frac{5}{12}x-\frac{17}{6}=-3$$

Add \frac{17}{6} to both sides.

$$\frac{5}{12}x=-3+\frac{17}{6}$$

Convert -3 to fraction -\frac{18}{6}.

$$\frac{5}{12}x=-\frac{18}{6}+\frac{17}{6}$$

Since -\frac{18}{6} and \frac{17}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{12}x=\frac{-18+17}{6}$$

Add -18 and 17 to get -1.

$$\frac{5}{12}x=-\frac{1}{6}$$

Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.

$$x=-\frac{1}{6}\times \frac{12}{5}$$

Multiply -\frac{1}{6} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-12}{6\times 5}$$

Do the multiplications in the fraction \frac{-12}{6\times 5}.

$$x=\frac{-12}{30}$$

Reduce the fraction \frac{-12}{30} to lowest terms by extracting and canceling out 6.

$$x=-\frac{2}{5}$$