Solve 1/4(x-10)=2/3x-5

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

Solve for x

$$x=6$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by x-10.

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

Multiply \frac{1}{4} and -10 to get \frac{-10}{4}.

$$\frac{1}{4}x+\frac{-10}{4}=\frac{2}{3}x-5$$

Reduce the fraction \frac{-10}{4} to lowest terms by extracting and canceling out 2.

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

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

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

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

$$-\frac{5}{12}x-\frac{5}{2}=-5$$

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

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

Convert -5 to fraction -\frac{10}{2}.

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

Since -\frac{10}{2} and \frac{5}{2} have the same denominator, add them by adding their numerators.

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

Add -10 and 5 to get -5.

$$-\frac{5}{12}x=-\frac{5}{2}$$

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

$$x=-\frac{5}{2}\left(-\frac{12}{5}\right)$$

Multiply -\frac{5}{2} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\left(-12\right)}{2\times 5}$$

Do the multiplications in the fraction \frac{-5\left(-12\right)}{2\times 5}.

$$x=\frac{60}{10}$$

Divide 60 by 10 to get 6.

$$x=6$$